EX-5.1

Exhibit 5.1

[Prosperity Bancshares, Inc. Letterhead]

September 30, 2025

Prosperity Bancshares, Inc.

4295 San Felipe

Houston, Texas 77027

Re: Registration Statement on Form S-4

Ladies and Gentlemen:

I am Executive Vice President and General Counsel to Prosperity Bancshares, Inc., a Texas corporation (“Prosperity”), and am providing this opinion in connection with the Registration Statement on Form S-4 (as amended, the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”), relating to the registration under the Securities Act of 1933, as amended (the “Securities Act”), of up to 4,439,981 shares of common stock, par value $1.00 per share, of Prosperity (the “Shares”) to be issued in connection with the transactions contemplated by the Agreement and Plan of Merger, dated as of July 17, 2025, by and between Prosperity and American Bank Holding Corporation, a Texas corporation (“American”) (as it may be amended from time to time, the “Merger Agreement”), pursuant to which American will merge with and into Prosperity, with Prosperity as the surviving corporation.

In rendering this opinion, I have examined the Registration Statement and the Merger Agreement and such corporate records, other documents and matters of law as I have deemed necessary or appropriate. In rendering this opinion, I have relied, with your approval, upon oral and written representations of other officers of Prosperity and certificates of other officers of Prosperity and public officials with respect to the accuracy of the factual matters addressed in such representations and certificates. In addition, in making such examination and rendering this opinion, I have assumed without verification the genuineness of all signatures, the authenticity of all documents submitted to me as originals, the conformity of certified copies submitted to me with the original documents to which such certified copies relate and the legal capacity of all individuals executing any of the foregoing documents.

Based on and subject to the foregoing, and subject to the qualifications, assumptions and limitations stated herein, I am of the opinion that the Shares are or will be, upon issuance, duly authorized and, when the Registration Statement has been declared effective by order of the Commission and if and when the Shares have been issued and delivered in the manner contemplated by and upon the terms and conditions set forth in the Registration Statement and the Merger Agreement, the Shares will be validly issued, fully paid and nonassessable.

The opinion set forth above is subject to the effects of (a) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting the enforcement of creditors’ rights generally, (b) general equitable principles (whether considered in a proceeding in equity or at law) and (c) an implied covenant of good faith and fair dealing.

I express no opinion as to whether, or the extent to which, the laws of any particular jurisdiction apply to the subject matter hereof. I am a member of the Bar of the State of Texas. This opinion is limited to the laws of the Texas as currently in effect, and I express no opinion as to the effect on the matters covered by this opinion of the laws of any other jurisdiction.

I hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and the references to my name therein, as well as under the heading “Legal Matters” in the related prospectus. In giving this consent, I do not thereby admit that I am within the category of persons whose consent is required by Section 7 of the Securities Act or the rules and regulations of the Commission thereunder. This opinion speaks as of its date, and I undertake no (and hereby disclaim any) obligation to update this opinion.

Very truly yours,

/s/ Charlotte M. Rasche

Charlotte M. Rasche