Exhibit 5.1

[Letterhead of Sullivan & Cromwell LLP]

April 23, 2021

M&T Bank Corporation,

    One M&T Plaza,

        Buffalo, New York 14203.

Ladies and Gentlemen:

In connection with the registration under the Securities Act of 1933 (the “Act”) of (1) 54,740,623 shares of common stock, par value $0.50 per share (the “Common Shares”), of M&T Bank Corporation, a New York corporation (the “Company”) and (2) 10,000,000 shares of Perpetual Fixed-to-Floating Rate Non-Cumulative Preferred Stock, Series H, par value $1.00 per share (the “Preferred Shares”), of the Company, we, as your counsel, have examined such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion. Upon the basis of such examination, we advise you that, in our opinion:

1.    When the registration statement relating to the Common Shares and the Preferred Shares (the “Registration Statement”) has become effective under the Act, and the Common Shares have been duly issued and delivered as provided in the Agreement and Plan of Merger, dated as of February 21, 2021, by and among the Company, People’s United Financial, Inc. a Delaware corporation, and Bridge Merger Corp., a Delaware corporation (the “Merger Agreement”), as contemplated by the Registration Statement, the Common Shares will be validly issued, fully paid and nonassessable.

2.     When the Registration Statement has become effective under the Act, the Certificates of Amendment to the Restated Certificate of Incorporation of the Company substantially in the forms attached as Annex B and Annex C to the joint proxy statement/prospectus contained in the Registration Statement have been duly filed with the New York Department of State, and the Preferred Shares have been duly issued and delivered as provided in the Merger Agreement, as contemplated by the Registration Statement, the Preferred Shares will be validly issued, fully paid and nonassessable.

In rendering the foregoing opinion, we are not passing upon, and assume no responsibility for, any disclosure in any registration statement or any related

prospectus or other offering material relating to the offer and sale of the Common Shares or the Preferred Shares.

The foregoing opinion is limited to the Federal laws of the United States and the laws of the State of New York, and we are expressing no opinion as to the effect of the laws of any other jurisdiction.

We have relied as to certain matters upon information obtained from public officials, officers of the Company and other sources believed by us to be responsible and we have assumed that the signatures on all documents examined by us are genuine, an assumption which we have not independently verified.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to us under the heading “Legal Matters” in the joint proxy statement/prospectus contained therein. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act.

Very truly yours,

/s/ Sullivan & Cromwell LLP