Exhibit 5.1

Goodwin Procter LLP 100 Northern Avenue Boston, MA 02210   goodwinlaw.com +1 617 570 1000

March 28, 2019

Unum Therapeutics Inc.

200 Cambridge Park Drive, Suite 3100

Cambridge, MA 02140

Re: Securities Being Registered under Registration Statement on Form S-8

Ladies and Gentlemen:

We have acted as counsel to you in connection with your filing of a Registration Statement on Form S-8 (as amended or supplemented, the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), on or about the date hereof relating to an aggregate of 1,502,899 shares (the “Shares”) of Common Stock, $0.001 par value per share, of Unum Therapeutics Inc., a Delaware corporation (the “Company”), that may be issued pursuant to the Company’s 2018 Stock Option and Incentive Plan and the Company’s 2018 Employee Stock Purchase Plan (collectively, the “Plans”).

We have reviewed such documents and made such examination of law as we have deemed appropriate to give the opinions set forth below. We have relied, without independent verification, on certificates of public officials and, as to matters of fact material to the opinion set forth below, on certificates of officers of the Company.

The opinion set forth below is limited to the Delaware General Corporation Law.

For purposes of the opinion set forth below, we have assumed that a sufficient number of authorized but unissued shares of the Company’s Common Stock will be available for issuance when the Shares are issued.

Based on the foregoing, we are of the opinion that the Shares have been duly authorized and, upon issuance and delivery against payment therefor in accordance with the terms of the Plans, will be validly issued, fully paid and nonassessable.

We hereby consent to the inclusion of this opinion as Exhibit 5.1 to the Registration Statement. In giving our consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/S/ GOODWIN PROCTER LLP

GOODWIN PROCTER LLP