Iberiabank (IBKC) 8-K Material Modifications to Rights of Security Holders

[LETTERHEAD OF JONES WALKER LLP]

EXHIBIT 5.1

April 4, 2019

IBERIABANK Corporation

200 West Congress Street

Lafayette, Louisiana 70501

Ladies and Gentlemen:

We have acted as special counsel to IBERIABANK Corporation, a Louisiana corporation (the “Company”), in connection with the offering of an aggregate of 4,000,000 depositary shares (the “Depositary Shares”), each representing a 1/400th ownership interest in a share of the Company’s 6.100%Fixed-to-FloatingNon-Cumulative Perpetual Preferred Stock, Series D, par value $1.00 per share (the “Series D Preferred Stock”), with a liquidation preference of $10,000 per share of Series D Preferred Stock (equivalent to $25 per Depositary Share) and representing an aggregate of 10,000 shares (the “Shares”) of the Series D Preferred Stock, pursuant to the Underwriting Agreement, dated March 28, 2019 (the “Underwriting Agreement”) among the Company and Merrill Lynch, Pierce, Fenner & Smith Incorporated and Keefe, Bruyette & Woods, Inc., as representatives of the several other underwriters named in Schedule A to the Underwriting Agreement. The Shares are to be deposited against delivery of a depositary receipt (the “Depositary Receipt”) representing the Depositary Shares to be issued by Computershare Trust Company, N.A. and Computershare Inc. (together, the “Depository”) under a Deposit Agreement, dated as of April 4, 2019 (the “Deposit Agreement”), among the Company, the Depository and holders from time to time of the Depositary Shares issued thereunder.

We have examined the Registration Statement on FormS-3 (FileNo. 333-230561) (the “Registration Statement”) filed by the Company on March 28, 2019 under the Securities Act of 1933, as amended; the Articles of Amendment to the Articles of Incorporation of the Company establishing the terms of the Series D Preferred Stock filed with the Secretary of State of the State of Louisiana; and the Deposit Agreement. We also have examined a copy of a global Depositary Receipt representing the Depositary Shares. In addition, we have examined, and have relied as to matters of fact upon, originals, or duplicates or certified or conformed copies, of such records, agreements, documents and other instruments and such certificates or comparable documents of public officials and of officers and representatives of the Company, and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth.

In such examination, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies and the authenticity of the originals of such latter documents.

In rendering the opinions set forth below, we have assumed that the Deposit Agreement has been duly authorized, executed and delivered by the Depository and is the valid and legally binding obligation of the Depository, that the Depositary Receipts have been duly issued against deposit of the Shares with the Depository in accordance with the Deposit Agreement, that the certificate evidencing the Depositary Receipts conforms to the specimen thereof examined by us, and that the Depositary Receipts have been duly executed and delivered by the Depository.

Upon the basis of such examination and assumptions, it is our opinion that the Shares have been validly issued and are fully paid and nonassessable, and the Depositary Receipts evidencing the Depositary Shares have been validity issued and entitle the holders thereof to the rights specified in the Depositary Receipts and the Deposit Agreement, in each case subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

We do not express any opinion herein concerning any law other than the laws of the State of Louisiana, the State of New York and the federal law of the United States (including the statutory provisions, all applicable provisions of the Louisiana Constitution and reported judicial decisions interpreting the foregoing).

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Company’s Current Report on Form8-K filed on April 4, 2019, and to the use of our name under the caption “Legal Matters” in the prospectus relating to the Shares and the Depositary Shares included in the Registration Statement.

Very truly yours,

/s/ Jones Walker LLP

Jones Walker LLP