Exhibit 5.1

One International Place, 40th Floor 100 Oliver Street Boston, MA 02110-2605 +1 617 728 7100 Main +1 617 426 6567 Fax www.dechert.com

June 16, 2021

Eagle Point Credit Company Inc.

600 Steamboat Road, Suite 202

Greenwich, CT 06830

Ladies and Gentlemen:

We have acted as counsel to Eagle Point Credit Company Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of a registration statement on Form N-2 (File Nos. 333-237586 and 811-22974) as originally filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) on April 6, 2020 under the Securities Act of 1933, as amended (the “Securities Act”), and under the Investment Company Act of 1940, as amended (the “Investment Company Act”), and the pre-effective amendment thereto filed by the Company with the Commission on May 29, 2020 under the Securities Act and Investment Company Act (the registration statement, as amended, at the time when it most recently became effective, including the prospectus and the information deemed to be part thereof at the time of effectiveness pursuant to Rule 430B of the Commission under the Securities Act, being hereinafter referred to collectively as the “Registration Statement”), and the final prospectus supplement, dated June 10, 2021 (including the base prospectus filed therewith, the “Prospectus Supplement”), filed with the Commission on June 11, 2021 pursuant to Rule 424 under the Securities Act, relating to the proposed issuance by the Company of 1,060,000 shares of its 6.50% Series C Term Preferred Stock Due 2031, $0.001 par value per share (the “Shares”), and up to 140,000 Shares that may be sold pursuant to the underwriters’ overallotment option, to be sold to underwriters pursuant to an underwriting agreement in substantially the form filed as Exhibit 1.1 to the Company’s Current Report on Form 8-K filed with the Commission on June 16, 2021 (the “Underwriting Agreement”). This opinion letter is being furnished to the Company in accordance with the requirements of Item 25 of Form N-2 under the Investment Company Act, and we express no opinion herein as to any matter other than as to the legality of the Shares.

In rendering the opinions expressed below, we have examined and relied on originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records and other instruments and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for rendering the opinions set forth below, including the following documents:

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As to the facts upon which this opinion is based, we have relied, to the extent we deem proper, upon certificates of public officials and certificates and written statements of agents, officers, directors, employees and representatives of the Company without having independently verified such factual matters.

In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as original documents and the conformity to original documents of all documents submitted to us as copies. In addition, we have assumed (i) the legal capacity of natural persons who are signatories to the documents examined by us and (ii) the legal power and authority of all persons signing on behalf of the parties to such documents (other than the Company).

On the basis of the foregoing and subject to the assumptions and qualifications set forth in this letter, we are of the opinion that: when (i) the Underwriting Agreement has been duly executed and delivered by the parties thereto and (ii) the Shares are (a) issued and delivered against receipt by the Company of payment therefor of such lawful consideration as the Board (or a duly authorized committee thereof) may lawfully determine and at a price per Share not less than the par value per Share as contemplated by the Registration Statement and the prospectus contained therein and in accordance with the terms of the Underwriting Agreement and (b) if applicable, countersigned by the transfer agent, the Shares will be validly issued, fully paid and nonassessable.

The opinions expressed herein are limited to the federal laws of the United States of America, the laws of the State of New York and the General Corporation Law of the State of Delaware. We are members of the bar of the State of New York.

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This opinion letter has been prepared solely in connection with the Registration Statement. The opinions expressed herein are based on laws in effect on the date hereof, which laws are subject to change with possible retroactive effect, and facts known to us on the date hereof. We assume no obligation to advise you of any changes in the foregoing subsequent to the date of this opinion.

We hereby consent to the filing of this opinion as an exhibit to the Company’s Current Report on Form 8-K filed with the Commission on June 16, 2021 and to the reference to this firm under the caption “Legal Matters” in the prospectus which forms a part of the Registration Statement and the Prospectus Supplement. In giving such consent, we do not thereby 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 of the Commission thereunder.

Very truly yours,

/s/ Dechert LLP