Exhibit 5.1

October 30, 2019

Board of Directors

Prosperity Bancshares, Inc.

Prosperity Bank Plaza

4295 San Felipe

Houston, Texas 77027

Ladies and Gentlemen:

We have acted as counsel to Prosperity Bancshares, Inc., a Texas corporation (“Prosperity”), in connection with (i) the Registration Statement on Form S-4 (File No. 333-233443), as amended (the “Initial Registration Statement”), filed by Prosperity with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the issuance of up to 26,250,000 shares of its common stock, par value $1.00 per share (“Common Stock”), and (ii) the related Registration Statement on Form S-4 (the “462(b) Registration Statement” and, together with the Initial Registration Statement, the “Registration Statements”) filed by Prosperity with the Commission on the date hereof pursuant to Rule 462(b) promulgated under the Securities Act, relating to the issuance of up to an additional 60,000 shares (the “Additional Shares”) of Common Stock. The 462(b) Registration Statement incorporates by reference the Initial Registration Statement that was declared effective by the Commission on September 17, 2019. The Additional Shares are proposed to be offered to the shareholders of LegacyTexas Financial Group, Inc., a Maryland corporation (“Legacy”), in connection with the merger of Legacy with and into Prosperity pursuant to the terms of the Agreement and Plan of Reorganization, dated as of June 16, 2019 (the “Merger Agreement”), by and between Prosperity and Legacy.

We have examined originals or copies of (i) the Registration Statements, (ii) the Merger Agreement, (iii) the Amended and Restated Articles of Incorporation of Prosperity, as amended to date, (iv) the Amended and Restated Bylaws of Prosperity, as amended to date, (v) certain resolutions adopted by the Board of Directors of Prosperity, and (vi) such other documents and records as we have deemed necessary and relevant for the purposes hereof. In addition, we have relied on certificates of officers of Prosperity and of public officials and others as to certain matters of fact relating to this opinion and have made such investigations of law as we have deemed necessary and relevant as a basis hereof. In the course of such examinations and investigations, we have assumed the genuineness of all signatures, the authenticity of all documents and records submitted to us as originals, the conformity to original documents and records of all documents and records submitted to us as copies, and the truthfulness of all statements of fact contained therein.

AUSTIN  CONNECTICUT  DALLAS  DUBAI  HOUSTON  LONDON  NEW YORK   SAN ANTONIO  SEATTLE  WASHINGTON, DC

Based on the foregoing and subject to the limitations, assumptions and qualifications set forth herein, and having due regard for such legal considerations as we deem relevant, we are of the opinion that the Additional Shares have been duly authorized for issuance, and if the Registration Statements are and remain effective under the Securities Act and if and when the Additional Shares are issued in accordance with the terms and conditions, and for the consideration, set forth in the Merger Agreement, the Additional Shares will be validly issued, fully paid and non-assessable.

The foregoing opinion is based on and is limited to the Texas Business Organizations Code (including the applicable provisions of the Texas Constitution and the reported judicial decisions interpreting those laws currently in effect) and the applicable federal laws of the United States of America, and we render no opinion with respect to the laws of any other jurisdiction.

In rendering the foregoing opinion, we are not passing upon, and assume no responsibility for, any disclosure in any registration statement or any related prospectus or other offering material related to the offer and sale of the Additional Shares.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the 462(b) Registration Statement and to the references to our firm under the heading “Legal Matters” in the joint proxy statement/prospectus included in the Initial Registration Statement. In giving such consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

AUSTIN  CONNECTICUT  DALLAS  DUBAI  HOUSTON  LONDON  NEW YORK   SAN ANTONIO  SEATTLE  WASHINGTON, DC