EX-5.1

Exhibit 5.1

LOGO

April 21, 2020

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 (the “Company”), in connection with the preparation of the Company’s Registration Statement on Form S-8 (the “Registration Statement”) as filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the proposed offer and sale to certain employees, directors and consultants of the Company of up to 2,500,000 shares (the “Shares”) of the Company’s common stock, par value $1.00 per share (the “Common Stock”), which are issuable pursuant to awards granted under the Prosperity Bancshares, Inc. 2020 Stock Incentive Plan (the “Plan”).

In connection with rendering this opinion, we have examined originals or copies identified to our satisfaction of (1) the Registration Statement; (2) the Amended and Restated Articles of Incorporation of the Company, as amended; (3) the Amended and Restated Bylaws of the Company, as amended; (4) the Plan; and (5) certain resolutions of the Board of Directors of the Company. We also have made such investigations of law and examined originals or copies of such other documents and records as we have deemed necessary and relevant as a basis for the opinions hereinafter expressed. In giving such opinion, we have relied upon certificates and representations of officers of the Company, of governmental and public officials and of other sources believed by us to be responsible with respect to the accuracy of the factual matters contained therein or covered thereby. We have assumed that the signatures on all documents examined by us are genuine, all documents submitted to us as originals are authentic and all documents submitted as certified or photostatic copies conform to the originals thereof.

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, when issued by the Company pursuant to the provisions of the Plan following due authorization of a particular award thereunder by the Board of Directors of the Company or a duly constituted and acting committee thereof (the “Board”) as provided in and in accordance with the Plan, the Shares issuable pursuant to such award will have been duly authorized by all necessary corporate action on the part of the Company; and, upon issuance and delivery of such Shares from time to time pursuant to the terms of such award for the consideration established pursuant to the terms of the Plan and otherwise in accordance with the terms and conditions of such award, including, if applicable, the lapse of any restrictions relating thereto, the satisfaction of any performance conditions associated therewith and any requisite determinations by or pursuant to the authority of the Board as provided therein, and, in the case of stock options, the exercise

thereof and payment for such Shares as provided therein, for a consideration at least equal to the par value thereof, such Shares will be validly issued, fully paid and nonassessable.


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