Exhibit 5.1

LUSE GORMAN, PC

ATTORNEYS AT LAW

5335 WISCONSIN AVENUE, N.W., SUITE 780

WASHINGTON, D.C. 20015

TELEPHONE (202) 274-2000

FACSIMILE (202) 362-2902

www.luselaw.com

January 23, 2017

The Board of Directors

Evans Bancorp, Inc.

One Grimsby Drive

Hamburg, New York 14075

Ladies and Gentlemen:

We have acted as counsel to Evans Bancorp, Inc., a New York corporation (the “Company”), in connection with the offering of shares of common stock, par value $0.50 per share (the “Common Stock”), by the Company pursuant to the Underwriting Agreement, dated January 18, 2017 (the “Underwriting Agreement”), by and among the Company, its wholly-owned subsidiary, Evans Bank, National Association, and Sandler O’Neill & Partners, L.P., for itself and as representative of the several underwriters (together, the “Underwriters”). The Underwriting Agreement provides for the purchase by the Underwriters of 400,000 shares of the Company’s Common Stock and, at the option of the Underwriters, up to 60,000 additional shares of Common Stock pursuant to an option to purchase additional shares (collectively, the “Shares”). The Shares are being offered and sold by the Company pursuant to a prospectus supplement dated January 18, 2017, and the accompanying base prospectus dated April 22, 2016 (together, the “Prospectus”), that form part of the Company’s effective registration statement on Form S-3, as amended (File No. 333-210443) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended.

We have reviewed the Registration Statement, the Prospectus, the Underwriting Agreement, and the corporate proceedings of the Company with respect to the authorization of the issuance of the Shares. We have also examined originals or copies of such documents, corporate records, certificates of public officials and other instruments, and have conducted such other investigations of law and fact as we have deemed necessary or advisable for purposes of our opinion. In our examination, we have assumed, without verification, the genuineness of all signatures, the authenticity of all documents and instruments submitted to us as originals, and the conformity to the originals of all documents and instruments submitted to us as certified or conformed copies. The opinion expressed below is limited to New York Business Corporation Law.

The Board of Directors

Evans Bancorp, Inc.

January 23, 2017

Page 2

Based upon the foregoing, and subject to the assumptions, exceptions, limitations, and qualifications stated herein, we are of the opinion that, when issued, delivered, and paid for in the manner and in accordance with the terms set forth in the Registration Statement, the Prospectus, and the Underwriting Agreement, the Shares will be validly issued, fully paid, and nonassessable.

We hereby consent to our firm being referenced under the captions “Legal Matters” and “Legal Opinions” in the Prospectus, and to the inclusion of this opinion as an exhibit to the Registration Statement.