EX-5.1

Exhibit 5.1

LOGO

Hogan Lovells US LLP

Columbia Square

555 Thirteenth Street, NW

Washington, DC 20004

T +1 202 637 5600

F +1 202 637 5910

www.hoganlovells.com

January 22, 2020

Board of Directors

Cambridge Bancorp

1336 Massachusetts Avenue

Cambridge, MA 02138

Ladies and Gentlemen:

We are acting as counsel to Cambridge Bancorp, a Massachusetts corporation (the “Company”), in connection with its registration statement on Form S-4 (the “Registration Statement”), filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”), relating to the proposed offering of up to 1,477,645 shares of common stock, par value $1.00 per share of the Company (the “Shares”), in connection with the merger contemplated by the Agreement and Plan of Merger, dated as of December 5, 2019 (the “Merger Agreement”), by and among the Company, Cambridge Trust Company, a Massachusetts-chartered trust company, which is a commercial bank, Wellesley Bancorp, Inc., a Maryland corporation, and Wellesley Bank, a Massachusetts-chartered bank. 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.

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 opinion 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 pdfs). 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.

This opinion letter is based as to matters of law solely on the applicable provisions of the Massachusetts Business 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 that following (i) effectiveness of the Registration Statement, (ii) effectiveness of the merger pursuant to the Merger Agreement and (iii) issuance of the Shares in accordance with the terms and conditions of the Merger Agreement, the Shares will be validly issued, fully paid and nonassessable.

This opinion letter has been prepared for use in connection with the Registration Statement. We assume no obligation to advise of any changes in the foregoing subsequent to the effective date of the Registration Statement.

Hogan Lovells US LLP is a limited liability partnership registered in the District of Columbia. “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in: Alicante Amsterdam Baltimore Beijing Birmingham Boston Brussels Colorado Springs Denver Dubai Dusseldorf Frankfurt Hamburg Hanoi Ho Chi Minh City Hong Kong Houston Johannesburg London Los Angeles Luxembourg Madrid Mexico City Miami Milan Minneapolis Monterrey Moscow Munich New York Northern Virginia Paris Perth Philadelphia Rome San Francisco São Paulo Shanghai Silicon Valley Singapore Sydney Tokyo Warsaw Washington, D.C. Associated Offices: Budapest Jakarta Riyadh Shanghai FTZ Ulaanbaatar Zagreb. Business Service Centers: Johannesburg Louisville. Legal Services Center: Berlin. For more information see www.hoganlovells.com