R1 RCM (RCM) S-3ASR Automatic shelf registration

Exhibit 5.1

300 North LaSalle Chicago, IL 60654 United States   +1 312 862 2000   www.kirkland.com       Facsimile: +1 312 862 2200

September 8, 2022

R1 RCM Inc.

434 W. Ascension Way

6th Floor

Murray, UT 84123

Re: Registration Statement on Form S-3ASR

Ladies and Gentlemen:

We are acting as special counsel to R1 RCM Inc., a Delaware corporation (the “Company”), in connection with the proposed registration by the Company of 179,754,055 shares of its common stock, par value $0.01 per share, pursuant to a Registration Statement on Form S-3ASR, to be filed with the Securities and Exchange Commission (the “Commission”) on or about the date hereof under the Securities Act of 1933, as amended (the “Act”) (such Registration Statement, as amended or supplemented, is hereinafter referred to as the “Registration Statement”). All of the 179,754,055 shares to be registered pursuant to the Registration Statement (the “Shares”) are being offered by the selling stockholder named in the Registration Statement, including up to 40,464,855 shares to be issued upon exercise of the Warrant, dated as of February 16, 2016, by and between R1 RCM Holdco Inc. (f/k/a R1 RCM Inc.) (“Old R1”) and the selling stockholder (the “Warrant”), and to be sold by such selling stockholder (the “Warrant Shares”), subject to the terms and conditions contained in the Warrant Assignment and Assumption Agreement, dated as of June 21, 2022, by and among Old R1, the Company and the selling stockholder (the “Assignment Agreement.”)

In connection therewith, we have examined originals, or copies certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments as we have deemed necessary for the purposes of this opinion, including (i) the corporate and organizational documents of the Company, including the Amended and Restated Certificate of Incorporation of the Company, filed with the Secretary of State of the State of Delaware on June 21, 2022, (ii) minutes and records of the proceedings of the Company with respect to the sale of the Shares, (iii) the Warrant, (iv) the Assignment Agreement and (v) the Registration Statement and the exhibits thereto.

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R1 RCM Inc.

September 8, 2022

Page 2

For purposes of this opinion, we have assumed the authenticity of all documents submitted to us as originals, the conformity to the originals of all documents submitted to us as copies and the authenticity of the originals of all documents submitted to us as copies. We have also assumed the legal capacity of all natural persons, the genuineness of the signatures of persons signing all documents in connection with which this opinion is rendered, the authority of such persons signing on behalf of the parties thereto other than the Company, the due authorization, execution and delivery of all documents by the parties thereto other than the Company and that the Warrant Shares will be issued in accordance with the terms of the Warrant. We have not independently established or verified any facts relevant to the opinions expressed herein, but have relied upon statements and representations of officers and other representatives of the Company and others.

Based upon and subject to the foregoing qualifications, assumptions and limitations and the further limitations set forth below, we are of the opinion that

1. The Warrant Shares have been duly authorized and, when the Warrant Shares have been duly issued in accordance with the Warrant and the Assignment Agreement, and when the Warrant Shares are duly countersigned by the Company’s transfer agent and registrar, upon receipt by the Company of the consideration to be paid therefor, the Warrant Shares will be validly issued, fully paid and nonassessable.

2. The Shares (other than the Warrant Shares) have been duly authorized and are validly issued, fully paid and non-assessable.

Our opinion expressed above is subject to the qualification that we express no opinion as to the applicability of, compliance with, or effect of any laws except the General Corporation Law of the State of Delaware (including the statutory provisions, all applicable provisions of the Delaware constitution and reported judicial decisions interpreting the foregoing).

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our firm under the heading “Legal Matters” in the Registration Statement. In giving this consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission.

We do not find it necessary for the purposes of this opinion, and accordingly we do not purport to cover herein, the application of the securities or “Blue Sky” laws of the various states to the issuance and sale of the Shares.

R1 RCM Inc.

September 8, 2022

Page 3

This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. This opinion speaks only as of the date that the Registration Statement becomes effective under the Act and we assume no obligation to revise or supplement this opinion after the date of effectiveness should the General Corporation Law of the State of Delaware be changed by legislative action, judicial decision or otherwise after the date hereof.

Sincerely,

/s/ Kirkland & Ellis LLP

KIRKLAND & ELLIS LLP