Exhibit 5.1     Eversheds Sutherland (US) LLP 700 Sixth Street, NW, Suite 700 Washington, DC 20001-3980

November 3, 2021

New Mountain Finance Corporation 

787 Seventh Avenue, 48th Floor 

New York, NY 10019

Ladies and Gentlemen:

We have acted as counsel to New Mountain Finance Corporation, a Delaware corporation (the “Company”), in connection with the preparation and filing of a registration statement on Form N-2 (File No. 333-238554) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), which Registration Statement became effective upon its filing on May 21, 2020 pursuant to rule 462(e) under the Securities Act, relating to the public offering of securities of the Company that may be offered by the Company from time to time as set forth in the prospectus dated May 21, 2020, which forms a part of the Registration Statement (the “Prospectus”), and as may be set forth from time to time in one or more supplements to the Prospectus.

This opinion letter is rendered in connection with the issuance and sale from time to time, of shares of the Company’s common stock, par value $0.01 per share (the “Shares”), having an aggregate offering price of up to $250,000,000, as described in the prospectus supplement, dated as of November 3, 2021, filed with the Commission pursuant to Rule 424 under the Securities Act (the “Prospectus Supplement”). The Shares are to be sold by the Company pursuant to the at-the-market Equity Distribution Agreement, dated as of November 3, 2021, by and among the Company, New Mountain Finance Advisers BDC, L.L.C., and New Mountain Finance Administration, L.L.C., on the one hand, and B. Riley Securities, Inc. and Raymond James & Associates, on the other hand (the “Distribution Agreement”).

As counsel to the Company, we have participated in the preparation of the Registration Statement and the Prospectus Supplement, and have examined the originals or copies, certified or otherwise identified to our satisfaction as being true copies, of the following:

(i)           The Amended and Restated Certificate of Incorporation of the Company, as amended by the (a) Certificate of Change of Registered Agent and/or Registered Office thereto and (b) Certificate of Amendment to the Amended and Restated Certificate of Incorporation of the Company, certified as of a recent date by the Delaware Secretary of State;

(ii)           The Amended and Restated Bylaws of the Company, certified as of the date hereof by an officer of the Company;

(iii)          A Certificate of Good Standing with respect to the Company issued by the Delaware Secretary of State as of a recent date;

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With respect to such examination and our opinion expressed herein, we have assumed, without any independent investigation or verification, (i) the genuineness of all signatures on all documents submitted to us for examination, (ii) the legal capacity of all natural persons, (iii) the authenticity of all documents submitted to us as originals, (iv) the conformity to original documents of all documents submitted to us as conformed or reproduced copies and the authenticity of the originals of such copied documents, (v) that all certificates issued by public officials have been properly issued and (vi) the accuracy and completeness of all corporate records made available to us by the Company.

As to certain matters of fact relevant to the opinion in this opinion letter, we have relied upon certificates of officers of the Company and on the representations, warranties and covenants of the Company set forth in the Distribution Agreement. We have also relied on certificates of public officials (which we have assumed remain accurate as of the date of this opinion). We have not independently established the facts, or in the case of certificates of public officials, the other statements, so relied upon.

The opinion set forth below is limited to the effect of the Delaware General Corporation Law, in effect as of the date hereof, and we express no opinion as to the applicability or effect of any other laws of such jurisdiction or the laws of any other jurisdictions.  Without limiting the preceding sentence, we express no opinion as to any state securities or broker-dealer laws or regulations thereunder relating to the offer, issuance and sale of the Shares. This opinion letter has been prepared, and should be interpreted, in accordance with customary practice followed in the preparation of opinion letters by lawyers who regularly give, and such customary practice followed by lawyers who on behalf of their clients regularly advise opinion recipients regarding, opinion letters of this kind.

On the basis of and subject to the foregoing, and in reliance thereon, and subject to the limitations and qualifications set forth in this opinion letter, we are of the opinion that the Shares have been duly authorized and, when issued and delivered against payment therefor in accordance with the terms of the Distribution Agreement, will be validly issued, fully paid and non-assessable.

The opinion expressed in this opinion letter is (i) strictly limited to the matters stated in this opinion letter, and without limiting the foregoing, no other opinions are to be inferred and (ii) only as of the date of this opinion letter, and we are under no obligation, and do not undertake, to advise the Company or any other person or entity either of any change of law or fact that occurs, or of any fact that comes to our attention, after the date of this opinion letter, even though such change or such fact may affect the legal analysis or a legal conclusion in this opinion letter.

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We hereby consent to the filing of this opinion letter as an exhibit to the Company’s Current Report on Form 8-K filed with the Commission for incorporation by reference in the Registration Statement and to the reference to our firm in the “Legal Matters” section in the Registration Statement. We do not admit by giving this consent that we are in the category of persons whose consent is required under Section 7 of the Securities Act.