Triton International Limited (TRTN-PC) 8-K Triton International Announces Pricing of Public

Bermuda Office

Appleby (Bermuda)

Limited

Canon’s Court

22 Victoria Street

PO Box HM 1179

Hamilton HM EX

Bermuda

Tel +1 441 295 2244

Exhibit 5.1

Triton International Limited Victoria Place, 5th Floor 31 Victoria Street, Hamilton HM 10 Bermuda Email SReesDavies@applebyglobal.com   Direct Dial +1 441 298 3296 Tel +1 441 295 2244 Fax +1 441 292 8666   Your Ref   Appleby Ref 436544/0009/SRD/AK   21 January 2020

Dear Sirs

TRITON INTERNATIONAL LIMITED (COMPANY)

INTRODUCTION

This opinion as to Bermuda law is addressed to you in connection with the filing by the Company of a registration statement on FormS-3 (Registration Statement), with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (Securities Act), and the rules and regulations promulgated thereunder, in relation to: (a) the proposed offering by the Company of 6,000,000 6.875% Series D Cumulative Redeemable Perpetual Preference Shares, USD0.01 par value, with a liquidation preference of USD25.00 per share, of the Company (Preference Shares), as described in the Prospectus (as defined in the Schedule to this opinion) and (b) the documents listed in Part 1 of Schedule 1 (Documents).

OUR REVIEW

For the purposes of giving this opinion we have examined and relied upon the Documents and the documents listed in Part 2 of Schedule 1. We have not examined any other documents, even if they are referred to in the Documents.

For the purposes of giving this opinion we have carried out the Company Search and the Litigation Search described in Part 3 of Schedule 1.

In giving this opinion we have relied upon and assume the accuracy and completeness of the certificate of the secretary of the Company dated the date hereof and annexed hereto (Certificate), the contents of which we have not verified.

Appleby (Bermuda) Limited (the Legal Practice) is a company limited by shares incorporated in Bermuda and approved and recognised under the Bermuda Bar (Professional Companies) Rules 2009. “Partner” is a title referring to a director, shareholder or an employee of the Legal Practice. A list of such persons can be obtained from your relationship partner. Bermuda ● British Virgin Islands ● Cayman Islands ● Guernsey ● Hong Kong ● Isle of Man ● Jersey ● Mauritius ● Seychelles ● Shanghai

We have not made any other enquiries concerning the Company and in particular we have not investigated or verified any matter of fact or representation (whether set out in any of the Documents or elsewhere) other than as expressly stated in this opinion.

Unless otherwise defined herein, capitalised terms have the meanings assigned to them in the Prospectus or Schedule 1, as applicable.

LIMITATIONS

Our opinion is limited to, and should be construed in accordance with, the laws of Bermuda at the date of this opinion. We express no opinion on the laws of any other jurisdiction.

This opinion is limited to the matters stated in it and does not extend to, and is not to be extended by implication, to any other matters. We express no opinion on the commercial implications of the Documents or whether they give effect to the commercial intentions of the parties.

We consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement; as Bermuda attorneys, however, we are not qualified to opine on matters of law of any jurisdiction other than Bermuda, accordingly we do not admit to being an expert within the meaning of the Securities Act.

ASSUMPTIONS AND RESERVATIONS

We give the following opinions on the basis of the assumptions set out in Schedule 2 (Assumptions), which we have not verified, and subject to the reservations set out in Schedule 3 (Reservations).

OPINIONS

1. Incorporation and Status: The Company is incorporated as an exempted company limited by shares and existing under the laws of Bermuda and is a separate legal entity. The Company is in good standing with the Registrar of Companies of Bermuda.

2. Preference Shares: When duly issued and paid for pursuant to and in accordance with the terms of the Resolutions, and delivered against payment therefore in the circumstances referred to or summarised in the Prospectus, the Preference Shares will be validly issued, fully paid,non-assessable shares of capital of the Company.

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Bermuda ● British Virgin Islands ● Cayman Islands ● Guernsey ● Hong Kong ● Isle of Man ● Jersey ● Mauritius ● Seychelles ● Shanghai

Bermuda Office

Appleby (Bermuda)

Limited

Canon’s Court

22 Victoria Street

PO Box HM 1179

Hamilton HM EX

Bermuda

Tel +1 441 295 2244

3. Authorisation: The Company has taken all necessary corporate action to authorise the issuance of the Preference Shares pursuant to Bermuda law.

Yours faithfully

Appleby (Bermuda) Limited

Appleby (Bermuda) Limited (the Legal Practice) is a company limited by shares incorporated in Bermuda and approved and recognised under the Bermuda Bar (Professional Companies) Rules 2009. “Partner” is a title referring to a director, shareholder or an employee of the Legal Practice. A list of such persons can be obtained from your relationship partner. Bermuda ● British Virgin Islands ● Cayman Islands ● Guernsey ● Hong Kong ● Isle of Man ● Jersey ● Mauritius ● Seychelles ● Shanghai

SCHEDULE 1

Part 1

The Documents

1. A copy, in PDF format of a Registration Statement on FormS-3 (RegistrationNo. 333-220340 as filed with the SEC on 5 September 2019 (Registration Statement).

2. A copy, in PDF format of the prospectus issued by the Company dated 5 September 2017 (Base Prospectus) as supplemented by the prospectus supplement dated 16 January 2020 (Prospectus Supplement and together with the Base Prospectus,Prospectus).

3. An executed copy, in PDF format of the Underwriting Agreement dated 16 January 2020 made between the Underwriters (as defined therein) and the Company.

Part 2

Other Documents Examined

1. A certified copy of the certificate of incorporation of the Company dated effective 29 September 2015 (Certificate of Incorporation).

2. A certified copy of the memorandum of association andbye-laws of the Company adopted effective 12 July 2016 (Constitutional Documents).

3. A Certificate of Compliance, dated 21 January 2020 issued by the Registrar of Companies in respect of the Company (Certificate of Compliance).

4. Certified copies of the unanimous written resolutions of the board of directors of the Company dated 9 January 2020 (Board Resolutions), of the meeting of the Pricing Committee (as defined in the Board Resolutions) held on 15 January 2020, which include the certificate of designations (Certificate of Designations) for the Preference Shares attached thereto as Exhibit A (Committee Resolutions) and of the pricing committee representative dated 16 January 2020 (Committee Representative Resolutions, together with the Board Resolutions and the Committee Resolutions, theResolutions).

5. A copy of the results of the Litigation Search.

6. A copy of the results of the Company Search.

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7. Certified copies of the “Foreign Exchange Letter” issued by the Bermuda Monetary Authority in relation to the Company.

8. An executed copy, in PDF format, of the Certificate.

Part 3

Searches

1. Searches of the entries and filings shown and available for inspection in respect of the Company in the register of charges and on the file of the Company maintained in the register of companies at the office of the Registrar of Companies in Hamilton, Bermuda, as revealed by searches conducted on 21 January 2020 (CompanySearch).

2. Searches of the entries and filings shown and available for inspection in respect of the Company in the Cause and Judgement Book of the Supreme Court maintained at the Registry of the Supreme Court in Hamilton, Bermuda, as revealed by searches conducted on 21 January 2020 (Litigation Search).

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SCHEDULE 2

Assumptions

We have assumed:

1. (i) that the originals of all documents examined in connection with this opinion are authentic, accurate and complete; and (ii) the authenticity, accuracy completeness and conformity to original documents of all documents submitted to us as copies;

2. that each of the Documents and other documentation which was received by electronic means is complete, intact and in conformity with the transmission as sent;

3. that there has been no change to the information contained in the Certificate of Incorporation and that the Constitutional Documents remain in full force and effect and are unamended;

4. that the signatures, initials and seals on all documents and certificates submitted to us as originals or copies of executed originals are authentic, and the signatures and initials on any Document executed by the Company are the signatures and initials of a person or persons authorised to execute the documents by the Company, by resolution of its board of directors or any power of attorney granted by the Company, to execute such Document;

5. that each of the parties (other than the Company under Bermuda law) is incorporated, organised or registered (as the case may be) and in good standing (where such concept is legally relevant) under the laws which govern its capacity and has the capacity, power and authority, has fulfilled all internal authorisation procedures and completed all applicable filings and formalities, and has obtained all authorisations, approvals, consents, licences and exemptions required under the laws of any relevant jurisdiction to execute, deliver and perform its respective obligations under the Documents, as applicable, and the transactions contemplated thereby and has taken all necessary corporate and other action required and completed all applicable formalities required to authorise the execution of the Documents, as applicable, and the performance of its obligations thereunder, as applicable;

6. the truth, accuracy and completeness of all representations and warranties or statements of fact or law (other than as to the laws of Bermuda in respect of matters upon which we have expressly opined) made in the Documents;

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7. the accuracy, completeness and currency of the records and filing systems maintained at the public offices where we have searched or enquired or have caused searches or enquiries to be conducted, that such search and enquiry did not fail to disclose any information which had been filed with or delivered to the relevant body but had not been processed at the time when the search was conducted and the enquiries were made, and that the information disclosed by the Company Search and the Litigation Search is accurate and complete in all respects and such information has not been materially altered since the date and time of the Company Search and the Litigation Search;

8. that there are no provisions of the laws or regulations of any jurisdiction other than Bermuda which would be contravened by the issuance of the Preference Shares or which would have any implication in relation to the opinion expressed herein and that, in so far as any obligation to be performed or action to be taken as described in the Registration Statement is required to be performed or taken in any jurisdiction outside Bermuda, the performance of such obligation or the taking of such action will constitute a valid and binding obligation of each of the parties thereto under the laws of that jurisdiction and will not be illegal by virtue of the laws of that jurisdiction;

9. that (i) the Documents are in the form of the documents approved in the Resolutions; (ii) any meetings at which such Resolutions were passed were duly convened and had a duly constituted quorum present and voting throughout; (iii) all interests of the directors of the Company on the subject matter of the Resolutions, if any, were declared and disclosed in accordance with the law and relevant Constitutional Documents; (iv) the Resolutions have not been revoked, amended or superseded, in whole or in part, and remain in full force and effect at the date of this opinion; and (v) the directors of the Company have concluded that the entry by the Company into the Documents, as applicable, and such other documents approved by the Resolutions and the transactions contemplated thereby arebona fide in the best interests of the Company and for a proper purpose of the Company, as applicable; and

10. that there is no matter affecting the authority of the directors to effect the issuance of the Preference Shares by the Company in accordance with the terms of the Prospectus and the Resolutions including breach of duty or lack of good faith which would have any adverse implications in relation to the opinions expressed in this opinion;

11. that the Company has filed the Prospectus in good faith for the purpose of carrying on its business and that at the time it did so, there were reasonable grounds for believing that the activities contemplated by the Prospectus would benefit the Company;

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12. that, save for the documents provided to us, there are no resolutions, agreements, documents or arrangements which materially affect, amend or vary the transactions envisaged in the Prospectus; and

13. that no resolution to voluntarily wind up the Company has been adopted by the members and no event of a type which is specified in the Constitutional Documents as giving rise to the winding up of the Company (if any) has in fact occurred.

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SCHEDULE 3

Reservations

Our opinion is subject to the following:

1. Good Standing: The term “good standing” means that the Company has received a Certificate of Compliance from the Registrar of Companies.

2. Non-Assessable: Any reference in this opinion to shares beingnon-assessable shall mean, in relation to fully-paid shares of the Company and subject to any contrary provision in any agreement in writing between the Company and the holder of shares, that: no shareholder shall be obliged to contribute further amounts to the capital of the Company, either in order to complete payment for their shares, to satisfy claims of creditors of the Company, or otherwise; and no shareholder shall be bound by an alteration of the memorandum of association orbye-laws of the Company after the date on which he became a shareholder, if and so far as the alteration requires him to take, or subscribe for additional shares, or in any way increases his liability to contribute to the share capital of, or otherwise to pay money to, the Company.

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