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EXHIBIT 5.1

OPINION OF DAVIS POLK & WARDWELL LLP

May 31, 2023

SS&C Technologies Holdings, Inc.
80 Lamberton Road

Windsor, Connecticut

Ladies and Gentlemen:

We have acted as special counsel to SS&C Technologies Holdings, Inc., a Delaware corporation (the “Company”), and are delivering this opinion in connection with the Company’s Registration Statement on Form S-8 (the “Registration Statement”) filed with the Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended, for the registration of 14,405,399 shares (the “Shares”) of the Company’s Common Stock, par value $0.01 per share, issuable pursuant to the SS&C Technologies Holdings, Inc. 2023 Stock Incentive Plan (the “Plan”).

We, as your counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

In rendering the opinion expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all signatures on all documents that we reviewed are genuine, (iv) all natural persons executing documents had and have the legal capacity to do so, (v) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate and (vi) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate.

On the basis of the foregoing, we are of the opinion that the Shares have been duly authorized and, when and to the extent issued pursuant to the Plan upon receipt by the Company of the consideration for the Shares specified therein, will be validly issued, fully paid and non-assessable.

We are members of the Bar of the State of New York and the foregoing opinion is limited to the laws of the State of New York and the General Corporation Law of the State of Delaware.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Davis Polk & Wardwell LLP