Troutman Pepper Hamilton Sanders LLP
401 9th Street NW, Suite 1000
Washington, DC 20004
troutman.com

May 26, 2023

Board of Directors

Burke & Herbert Financial Services Corp.

100 S. Fairfax Street

Alexandria, VA 22314

Re: Registration Statement on Form S-8

Ladies and Gentlemen:

We are acting as counsel to Burke & Herbert Financial Services Corp., a Virginia corporation (the "Company"), in connection with the preparation and filing of its registration statement on Form S-8 (the "Registration Statement"), filed as of the date hereof with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the "Act"), relating to the registration of 644,025 shares (the "Shares") of the Company's common shares, par value $0.50 per share (the "Common Shares"), 250,000 of which may be issued pursuant to each of the Burke & Herbert Financial Services Corp. 2023 Employee Stock Purchase Plan and the Burke & Herbert Financial Services Corp. 2023 Stock Incentive Plan, and 144,025 of which may be issued pursuant to the Burke & Herbert Financial Services Corp. 2019 Stock Incentive Plan, As Amended October 27, 2022 (the "Plans"). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus, other than as expressly stated herein with respect to the issuance of the Shares.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including telecopies). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters.

This opinion letter is based as to matters of law solely on the Virginia Stock Corporation Act, as amended. We express no opinion herein as to any other statutes, rules or regulations. Based upon, subject to and limited by the foregoing, we are of the opinion as of the date hereof, when the Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the recipients, and have been issued by the Company for legal consideration in excess of par value in the

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circumstances contemplated by the Plans, assuming in each case that the individual issuances, grants or awards under the Plans are duly authorized by all necessary corporate action and duly issued, granted or awarded and exercised in accordance with the requirements of law and the Plans (and the agreements duly adopted thereunder and in accordance therewith), the issue and sale of the Shares will have been duly authorized by all necessary corporate action of the Company and the Shares will be validly issued, fully paid, and nonassessable.

This opinion letter has been prepared for use in connection with the Registration Statement and is made as of the date hereof and is subject to, and may be limited by, future changes in the factual matters set forth herein. We assume no obligation to advise you of any changes in the foregoing subsequent to the delivery of this opinion letter. Further, the opinions expressed herein are based upon the law in effect (and published or otherwise generally available) on the date hereof, and we assume no obligation to revise or supplement these opinions should such law be changed by legislative action, judicial decision or otherwise. In rendering our opinions, we have not considered, and hereby disclaim any opinion as to, the application or impact of any laws, cases, decisions, rules or regulations of any other jurisdiction, court or administrative agency.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement. In giving this consent, we do not thereby admit that we are an "expert" within the meaning of the Act.

Very truly yours,

/s/ Troutman Pepper Hamilton Sanders LLP

Troutman Pepper Hamilton Sanders LLP

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