Broadcom Cayman 8-K Other Events

Exhibit 5.1

[On the letterhead of Allen & Gledhill LLP]

27 January 2017

Broadcom Limited

1 Yishun Avenue 7

Singapore 768923

Dear Sirs

Broadcom Limited — Prospectus Supplement Filed Pursuant to Rule 424(B) Under the Securities Act (As Defined Herein) In Respect of the Ordinary Shares (As Defined Herein)

1. Introduction

1.1 We refer to the prospectus supplement dated on or around the date hereof (the “Prospectus Supplement”) to the prospectus dated March 4, 2016 (the “Prospectus”) included in the Company’s Registration Statement on FormS-3 (FileNo. 333-205938) (as amended, including the documents incorporated by reference therein, the “Registration Statement”) filed by Broadcom Limited (the “Company”), a company incorporated under the laws of the Republic of Singapore, with the United States Securities and Exchange Commission in connection with the registration under the Securities Act of 1933 (the “Securities Act”), as amended, of up to 22,804,591 ordinary shares in the capital of the Company (such shares, the “OrdinaryShares”) which may be allotted and issued, from time to time, by the Company in exchange for exchangeable limited partnership units of Broadcom Cayman L.P. (the “Exchangeable Units”). The Exchangeable Units were issued in connection with the merger of Avago Technologies Limited (“Avago”), a company incorporated under the laws of the Republic of Singapore and previously listed on the NASDAQ Global Select Market (“NASDAQ”), with Broadcom Corporation (“Broadcom”), a California corporation previously listed on NASDAQ, pursuant to an Agreement and Plan of Merger entered into by and among Avago, Broadcom, the Company, Safari Cayman L.P., now Broadcom Cayman L.P. (the “Partnership”), and the other parties thereto, dated as of May 28, 2015, as amended (the “Merger Agreement”).

1.2 This opinion is limited to Singapore law as applied by the Singapore courts and published and in effect on the date of this opinion. It is given on the basis that all matters relating to it will be governed by, and that it (including all terms used in it) will be construed in accordance with, Singapore law. We have made no investigation of, and do not express or imply any views on, the laws of any country other than Singapore or (except as otherwise expressly provided herein) any factual matters. This opinion is being rendered to you in connection with the filing of the Prospectus Supplement, is strictly limited to the matters stated in it and does not apply by implication to other matters.

2. Scope of Enquiry

2.1 For the purpose of rendering this opinion, we have examined:

2.1.1 an executed copy of the Merger Agreement as annexed to the Registration Statement on FormS-4 filed by the Company with the United States Securities and Exchange Commission under the Securities Act;

2.1.2 a copy of the Certificate Confirming Incorporation of Company dated 4 March 2015 issued by the Accounting and Corporate Regulatory Authority of Singapore (“ACRA”) confirming that the Company is incorporated under the Companies Act, Chapter 50 of Singapore (the “Companies Act”) on 3 March 2015 and the Notice of Incorporation Upon Change of Name of the Company dated 1 February 2016;

2.1.3 a copy of the Certificate Under Section 61(7) of the Companies Act dated 4 March 2015 issued by ACRA confirming that the necessary declaration required under the Companies Act has been lodged by the Company on 3 March 2015 and the Company is entitled to commence business;

2.1.4 a copy of the Constitution of the Company in force as at the date of this opinion;

2.1.5 a copy of the resolutions in writing of the Board of Directors of the Company passed on 29 January 2016 (excluding the exhibits thereto) (the “Board Resolutions”);

2.1.6 a copy of the resolutions passed by the sole shareholder of the Company on 31 January 2016 (excluding the exhibits thereto) (the “Shareholder Resolutions”); and

2.1.7 such other documents and matters as we have determined necessary or appropriate to render this opinion, subject to the assumptions, limitations and qualifications stated herein.

2.2 This opinion is limited to the documents referred to above and we have not examined any contract, instrument or other document entered into by or affecting the Company or any of the corporate records of the Company, and we have not made any other enquiries concerning the Company.

3. Assumptions

For the purpose of this opinion, we have assumed that:

3.1 copies of all documents referred to in paragraph 2.1 conform in all respects to the originals;

3.2 copies of all documents referred to in paragraph 2.1 above submitted to us for examination are true, complete andup-to-date copies;

3.3 each signature is the genuine signature of the individual concerned and all stamps and seals are genuine and affixed as prescribed in the Constitution of the Company;

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3.4 all facts stated in all documents referred to in paragraph 2.1 are correct;

3.5 each of the Board Resolutions and the Shareholder Resolutions have not been rescinded or modified and all authorisations and approvals conferred thereby remain in full force and effect and that no other resolution or other action has been taken which may affect the validity of those resolutions;

3.6 the Ordinary Shares which may, from time to time, be allotted and issued will be allotted and issued, and delivered, in accordance with the terms of the Merger Agreement, any other agreement relating to the Exchangeable Units, and the requirements under the Constitution of the Company and Singapore law; and

3.7 the share certificates in respect of the Ordinary Shares will be issued by the share registrar and transfer agent of the Company in accordance with the Constitution of the Company (as amended from time to time) and the Companies Act.

4. Opinion

4.1 Based on the documents referred to in paragraph 2.1 and the assumptions in paragraph 3, and subject to the qualifications set out below and any matters not disclosed to us, we are of the opinion that the Ordinary Shares which may be allotted and issued, from time to time, by the Company in exchange for the Exchangeable Units:

4.1.1 when represented by share certificates issued by the Company in respect of such Ordinary Shares; and

4.1.2 duly registered in the register of members of the Company, in the name of the persons entitled to be allotted and issued such Ordinary Shares, or in the name of Cede & Co., a partnership organized pursuant to the laws of the State of New York, in the United States of America, as nominee of the Depository Trust Company, as the case may be,

will be validly allotted and issued and credited as fully paid in accordance with the laws of Singapore andnon-assessable.

4.2 For the purposes of this opinion we have assumed that the term“non-assessable” (a term which has no recognised meaning under Singapore law) in relation to Ordinary Shares to be allotted and issued means under Singapore law that holders of such shares, having fully paid up all amounts due on such shares as to the issue price thereon, are under no further personal liability to contribute to the assets or liabilities of the Company in their capacities purely as holders of such shares.

5. Qualifications

This opinion is subject to the following qualifications:

5.1 this opinion is given on the basis that there will be no amendment to or termination or replacement of the documents, authorisations and approvals referred to in paragraph 2.1 of this opinion. We undertake no responsibility to notify the addressee of this opinion of any changes after the date of this opinion that may alter, affect or modify the opinion expressed herein; and

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5.2 this opinion is strictly limited to the matters stated herein and is not to be read as extending by implication to any other matter, including but without limitation, the Merger Agreement or any other document signed in connection therewith. In particular, we express no opinion on whether the allotment and issuance of securities pursuant to the exchange of the Exchangeable Units complies with the laws and regulations relating to the offering of securities in Singapore or any other jurisdiction.

6. Disclosure and Reliance

6.1 Subject to the foregoing, we consent to the use and filing of this opinion as an exhibit to the Company’s Current Report on Form8-K dated on or around the date hereof and filed by the Company (the “Company’s Form8-K”) and further consent to all references to us in the Prospectus Supplement and any amendments thereto. In giving this consent, we do not hereby admit and shall not be deemed to admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act.

6.2 In addition, save for the filing of this opinion as an exhibit to the Company’s Form8-K, this opinion is not to be circulated to, or relied upon by, any other person (other than persons entitled to rely on it pursuant to applicable provisions of federal securities law in the United States, if applicable) or quoted or referred to in any public document or filed with anyone without our prior written consent.

Yours faithfully

/s/ Allen & Gledhill LLP

Allen & Gledhill LLP

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