Exhibit 5.1

707 Torrance Boulevard Suite 200 Redondo Beach, CA 90227-3400 Telephone: (310) 540-3199 Facsimile: (310) 316-1823

ATTORNEYS AT LAW A PROFESSIONAL CORPORATION www.practicallawyer.com

Reply to Colorado Office: 5050 South Syracuse Street Suite 900 Denver, CO 80237 Telephone: (303) 792-3456 Facsimile: (303) 792-9092

April 22, 2026

Arrow Financial Corporation

250 Glen Street

Glen Falls, New York 12801

Ladies and Gentlemen,

We have acted as counsel to Arrow Financial Corporation, a New York corporation (the “Company”), in connection with the preparation and filing of the Registration Statement on Form S-4 (the “Registration Statement”) with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”). The Registration Statement relates to the registration under the Securities Act of shares of the Company’s common stock, par value $1.00 per share, (the “Shares”) to be issued pursuant to the Agreement and Plan of Merger, dated as of February 25, 2026, by and among the Company, Arrow Merger Sub, Inc., a Maryland corporation, and Adirondack Bancorp, Inc., a New York corporation (the “Merger Agreement”).

In rendering the opinions expressed below, we have reviewed originals or copies of the following documents (the “Documents”): (a) the Certificate of Incorporation and the Bylaws of the Company, in each case, as amended through the date hereof; (b) the resolutions of the Board of Directors of the Company, adopted on February 25, 2026, relating to the Merger Agreement, the filing of the Registration Statement, the issuance of the Shares and other matters; (c) the Merger Agreement; (d) the Registration Statement; (e) such other corporate records of the Company, certificates of public officials and of officers of the Company and agreements and other documents as we have deemed necessary as a basis for the opinion expressed below. In our review of the Documents we have assumed the genuineness of all signatures, the authenticity of the originals of the documents submitted to us, the conformity to authentic originals of any documents submitted to us as copies, as to matters of fact, the truthfulness of the representations made in certificates of public officials and officers of the Company, and the legal capacity of all individuals executing any of the foregoing documents.  We have not independently established the validity of the foregoing assumptions.

Based upon the foregoing and upon such other investigation as we have deemed necessary and subject to the qualifications set forth below, we are of the opinion that, when the Registration Statement relating to the Shares has become effective under the Securities Act and the Shares have been issued and delivered by the Company in accordance with the terms of the Merger Agreement and as contemplated by the Registration Statement, the Shares will be validly issued, fully paid and non-assessable.

Our opinion is limited to the federal laws of the United States and the laws of the State of New York and we do not express any opinion herein concerning any other law.

This opinion letter is provided solely in connection with the issuance of the Shares pursuant to the Registration Statement and is not to be relied upon for any other purpose.

Arrow Financial Corporation

April 22, 2026

Page 2

This opinion letter speaks only as of the date hereof. We expressly disclaim any responsibility to advise you of any development or circumstance of any kind, including any change of law or fact, that may occur after the date of this opinion letter that might affect the opinion expressed herein.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement and to the use of our name therein and in the prospectus included in the Registration Statement under the caption “Legal Matters.” In giving this consent, we do not hereby admit that we come within the category of persons whose consent is required under Section 7 of the Securities Act, or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Spierer, Woodward, Corbalis & Goldberg, PC