Exhibit 23.5

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the reference to our firm under the caption “Experts” in the Registration Statement on Form S-4 of Cambridge Bancorp and to the incorporation by reference therein of our report dated March 29, 2019, with respect to the consolidated financial statements of Wellesley Bancorp, Inc. included in its Annual Report on Form 10-K for the year ended December 31, 2018 filed with the Securities and Exchange Commission.

/s/ Wolf & Company P.C.

Boston, Massachusetts

January 22, 2020