Exhibit 5.1

Nicolas H.R. Dumont

+1 212 479 6446

ndumont@cooley.com

April 21, 2022

Core Scientific, Inc.

210 Barton Springs Road

Suite 300

Austin, TX 78704

Re: Core Scientific, Inc. – Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as counsel to Core Scientific, Inc., a Delaware corporation (the “Company”), with respect to certain matters in connection with the filing by the Company of a Registration Statement on Form S-1 (the “Registration Statement”) (No. 333-262596) with the Securities and Exchange Commission, including a related prospectus included in the Registration Statement (the “Prospectus”), covering the registration of (a) the issuance of shares of common stock, par value of $0.0001 per share (the “Common Stock”), of the Company upon the exercise of warrants issued by the Company, and (b) the resale of Common Stock and warrants to purchase Common Stock, as follows:

(i) the issuance of up to 6,266,667 shares (the “Private Warrant Shares”) of Common Stock upon the exercise of certain outstanding warrants (the “Private Warrants”) by the holders thereof;

(ii) the issuance of up to 8,625,000 shares (the “Public Warrant Shares” and, together with the Private Warrant Shares, the “Warrant Shares”) of Common Stock upon the exercise of certain outstanding warrants (the “Public Warrants” and, together with the Private Warrants, the “Warrants”) by the holders thereof;

(iii) the resale of 6,266,667 Private Warrants;

(iv) the resale of 3,200,306 warrants (the “Legacy Warrants” and together with the Private Warrants, the “Resale Warrants”) assumed by the Company that were initially issued by Core Scientific Holding Co. (the “Legacy Core”); and

(v) the resale of up to 230,923,357 shares of Common Stock (the “Selling Stockholder Shares”) consisting of:

• 8,625,000 shares of Common Stock issued in a private placement in connection with the Company’s initial public offering;

• 87,344,633 shares of Common Stock issued pursuant to that certain Agreement and Plan of Reorganization and Merger, dated as of July 20, 2021, as amended on October 1, 2021, and as further amended on December 29, 2021, by and among Core Scientific Holding Co., a Delaware corporation, XPDI Merger Sub Inc., a Delaware corporation, and the Company (f/k/a Power & Digital Infrastructure Acquisition Corp.);

• up to 6,266,667 Private Warrant Shares;

Cooley LLP    55 Hudson Yards    New York, NY    10001-2157

t: (212) 479-6000 f: (212) 479-6275 cooley.com

Core Scientific, Inc.

April 21, 2022

Page Two

• up to (i) 3,200,306 shares (the “Legacy Warrant Shares”) of Common Stock issuable upon the exercise of the Legacy Warrants, (ii) 24,962,264 shares of Common Stock issuable upon the settlement of restricted stock units, (iii) 811,917 outstanding shares of Common Stock underlying restricted stock awards that are subject to vesting and (iv) 18,819,555 shares of Common Stock issuable upon the exercise of stock options (collectively, the “Convertible Security Shares”) held by certain affiliates of the Company; and

• up to 80,893,015 shares (the “Conversion Shares”) of Common Stock issuable upon the conversion of certain convertible promissory notes (collectively, the “Convertible Notes”) assumed by the Company that were initially issued pursuant to (i) the Secured Convertible Note Purchase Agreement, dated as of April 19, 2021, as amended on April 22, 2021, and (ii) the Convertible Note Purchase agreement, dated as of August 20, 2021, as amended on September 23, 2021, each by and among Legacy Core, the guarantors thereto, the purchasers thereto and U.S. Bank National Association as note agent and collateral agent (collectively, the “Note Agreements”).

The Warrants were issued pursuant to a Warrant Agreement, dated as of February 9, 2021, by and between Power & Digital Infrastructure Acquisition Corp. and Continental Stock Transfer & Trust Company, as warrant agent (as amended, the “Warrant Agreement”).

In connection with this opinion, we have examined and relied upon (a) the Registration Statement and the Prospectus, (b) the Company’s certificate of incorporation and bylaws, each as currently in effect, (c) the Warrant Agreement, (d) the Warrants, (e) the Legacy Warrants, (f) the Note Agreements, (g) forms of Convertible Notes and (h) originals, or copies certified to our satisfaction, of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below. We have assumed the genuineness of all signatures; the authenticity of all documents submitted to us as originals; the conformity to originals of all documents submitted to us as copies; and the accuracy, completeness and authenticity of certificates of public officials and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

With respect to the Warrants, the Warrant Shares, the Legacy Warrants, the Legacy Warrant Shares and the Conversion Shares, we express no opinion to the extent that future issuances of securities of the Company, including the Warrant Shares, the Legacy Warrant Shares and the Conversion Shares, and/or antidilution adjustments to outstanding securities of the Company, including the Warrants, the Legacy Warrants and the Convertible Notes, cause the Warrants, the Legacy Warrants or the Convertible Notes to be exercisable for more shares of Common Stock than the number of shares of Common Stock that then remain authorized but unissued. Further, we have assumed that the exercise price of the Warrants and the Legacy Warrants and the conversion price of the Convertible Notes will not be adjusted to an amount below the par value per share of Common Stock.

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware and the laws of the State of New York. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

With regard to our opinion concerning the Resale Warrants constituting valid and binding obligations of the Company:

Cooley LLP    55 Hudson Yards    New York,    NY 10001-2157

t: (212) 479-6000 f: (212) 479-6275 cooley.com

Core Scientific, Inc.

April 21, 2022

Page Three

(i)      Our opinion is subject to, and may be limited by, (a) applicable bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance, debtor and creditor, and similar laws which relate to or affect creditors’ rights generally, and (b) general principles of equity (including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing) regardless of whether considered in a proceeding in equity or at law.

(ii)     Our opinion is subject to the qualification that the availability of specific performance, an injunction or other equitable remedies is subject to the discretion of the court before which the request is brought.

(iii)    We express no opinion as to any provision of the Resale Warrants that: (a) provides for liquidated damages, buy-in damages, monetary penalties, prepayment or make-whole payments or other economic remedies to the extent such provisions may constitute unlawful penalties; (b) relates to advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary requirements, statutes of limitations, trial by jury, or procedural rights; (c) restricts non-written modifications and waivers; (d) provides for the payment of legal and other professional fees where such payment is contrary to law or public policy; (e) relates to exclusivity, election or accumulation of rights or remedies; (f) authorizes or validated conclusive or discretionary determinations; or (g) provides that provisions of the Warrants are severable to the extent an essential part of the agreed exchange is determined to be invalid and unenforceable.

(iv)    We express no opinion as to whether a state court outside of the State of New York or a federal court of the United States would give effect to the choice of New York law provided for in the Resale Warrants.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that:

1. The Warrant Shares, when issued and paid for upon exercise of the Warrants in accordance with the terms of the Warrants, will be validly issued, fully paid and nonassessable.

2. The Resale Warrants constitute valid and binding obligations of the Company.

3. The Selling Stockholder Shares, other than any Private Warrant Shares, Convertible Security Shares (including Legacy Warrant Shares) or Conversion Shares included in the Selling Stockholder Shares, are validly issued, fully paid and non-assessable. Any Private Warrant Shares, Convertible Security Shares (including Legacy Warrant Shares) or Conversion Shares included in the Selling Stockholder Shares, when issued and paid for or vest in accordance with the terms of the Private Warrants, the applicable equity award agreements, the Legacy Warrants or the Convertible Notes, as applicable, will be validly issued, fully paid and nonassessable.

Our opinion is limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated. Our opinion is based on these laws as in effect on the date hereof, and we disclaim any obligation to advise you of facts, circumstances, events or developments which hereafter may be brought to our attention and which may alter, affect or modify the opinion expressed herein.

We hereby consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Registration Statement.

Cooley LLP    55 Hudson Yards    New York,    NY 10001-2157

t: (212) 479-6000 f: (212) 479-6275 cooley.com

Core Scientific, Inc.

April 21, 2022

Page Four

Sincerely,
COOLEY LLP
By:	/S/ NICOLAS H.R. DUMONT
	Nicolas H.R. Dumont

Cooley LLP    55 Hudson Yards    New York,    NY 10001-2157

t: (212) 479-6000 f: (212) 479-6275 cooley.com