Exhibit 5.1

609 Main Street Houston, TX 77002 United States   +1 713 836 3600   www.kirkland.com Facsimile:
+1 713 836 3601

December 1, 2023

Baker Hughes Company

Baker Hughes Holdings LLC

Baker Hughes Co-Obligor, Inc.

575 N. Dairy Ashford Rd., Suite 100

Houston, Texas 77079-1121

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We are issuing this opinion letter in our capacity as special counsel to Baker Hughes Company, a Delaware corporation (“Baker Hughes”), Baker Hughes Holdings LLC, a Delaware limited liability company (“BHH LLC”) and Baker Hughes Co-Obligor, Inc. a Delaware corporation (“Co-Obligor” and, together with BHH LLC and Baker Hughes, the “Registrants”), in connection with the preparation of the Registration Statement on Form S-3 (as amended or supplemented, the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) on December 1, 2023 under the Securities Act of 1933, as amended (the “Securities Act”), relating to Securities (as defined below) that may be issued and sold by the Registrants. The Registration Statement relates to the sale, from time to time, pursuant to Rule 415 of the General Rules and Regulations promulgated under the Securities Act, of an indeterminate amount of: (i) any combination of Baker Hughes’ (a) Class A common stock, par value $0.0001 per share (the “Class A common stock”), (b) preferred stock, par value $0.0001 per share (the “Preferred Stock”), (c) debt securities, in one or more series (the “Parent Debt Securities”), (d) full and unconditional guarantees of Subsidiary Debt Securities (as defined below) (the “Parent Guarantees”), (e) purchase contracts (the “Purchase Contracts”), warrants (the “Warrants”) and units (the “Units”); and (ii) any combination of BHH LLC’s and Co-Obligor’s (a) debt securities, in one or more series (the “Subsidiary Debt Securities” and, together with the Parent Debt Securities, the “Debt Securities”) and (b) guarantees of Parent Debt Securities, full and unconditional or otherwise (the “Subsidiary Guarantees” and, together with the Parent Guarantees, the “Guarantees” and, together with the Class A common stock, Preferred Stock, Debt Securities, Purchase Contracts, Warrants, and Units, the “Securities”). The Parent Debt Securities will be issued under an indenture (the “Parent Indenture”), or a supplement thereto, between Baker Hughes and a trustee named therein. Unless otherwise specified in the appropriate prospectus supplement, the Subsidiary Debt Securities will be issued under an indenture, dated as of October 28, 2008 (the “Subsidiary Base Indenture”), between Baker Hughes Incorporated (as predecessor to BHH LLC) and The Bank of New York Mellon Trust Company, N.A., as trustee (the “Trustee”), as amended and supplemented by the second supplemental indenture, dated July 3, 2017, among Baker Hughes, a GE Company, LLC (as predecessor to BHH LLC), Co-Obligor and the Trustee (the “Second Supplemental Indenture”). The Base Indenture, as amended and supplemented by the Second Supplemental Indenture, and as further amended and supplemented, is referred to herein as the “Subsidiary Indenture.”

In connection with the registration of the Securities, we have examined originals, or copies certified or otherwise identified to our satisfaction, of such documents, corporate or limited liability company records and other instruments as we have deemed necessary for the purposes of this opinion, including: (i) the corporate, limited liability company and other organizational documents, as applicable, of each Registrant, (ii) minutes and records of the corporate proceedings of each Registrant with respect to the issuance of the Securities, and (iii) the Registration Statement and the exhibits thereto.

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Baker Hughes Company

Baker Hughes Holdings LLC

Baker Hughes Co-Obligor, Inc.

December 1, 2023

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 Registrants and the due authorization, execution and delivery of all documents by the parties thereto other than the Registrants. We have not independently established or verified any facts relevant to the opinions expressed herein but have relied upon statements and representations of the officers and other representatives of each Registrant.

We have also assumed that:

(i) the Registration Statement and any amendment thereto (including post-effective amendments) will have become effective under the Securities Act and will comply with all applicable laws at the time the Securities are offered or issued as contemplated by the Registration Statement;

(ii) if applicable, a prospectus supplement or term sheet (“Prospectus Supplement”) will have been prepared and filed with the Commission describing the Securities offered thereby and will comply with all applicable laws;

(iii) all Securities will be offered, issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and, if applicable, the appropriate Prospectus Supplement;

(iv) the respective board of directors and the stockholders or the managing member, as applicable, of each Registrant will have taken all necessary corporate or limited liability company action to authorize the issuance of the Securities and any other Securities issuable on the conversion, exchange, redemption or exercise thereof, and to authorize the terms of the offering and the issuance and sale of such Securities and related matters;

(v) at the time of issuance of the Securities or Securities issuable upon conversion, exchange, redemption or exercise of any Securities being offered, each applicable Registrant will validly exist and be duly qualified and in good standing under the laws of its jurisdiction of formation and each such Registrant will have the necessary organizational power and authority to issue such Securities, or Securities issuable upon conversion, exchange, redemption or exercise of any Securities, as applicable;

(vi) any Securities issuable upon conversion, exchange, redemption or exercise of any Securities being offered will be duly authorized, created and, if appropriate, reserved for issuance upon such conversion, exchange, redemption or exercise;

(vii) a definitive purchase agreement, underwriting agreement, warrant agreement, purchase contract agreement, unit agreement or similar agreement with respect to any Securities offered will have been duly authorized and validly executed and delivered by each applicable Registrant and the other parties thereto (each, a “Purchase Agreement”);

Baker Hughes Company

Baker Hughes Holdings LLC

Baker Hughes Co-Obligor, Inc.

December 1, 2023

Page 3

(viii) all Securities, and any certificates in respect thereof, will be delivered either (a) in accordance with the provisions of the applicable Purchase Agreement approved by the respective board of directors or managing member, as applicable, of each applicable Registrant upon payment of consideration therefor provided for therein or (b) upon conversion, exchange, redemption or exercise of any other Security, in accordance with the terms of such Security or the instrument governing such Security providing for such conversion, exchange, redemption or exercise as approved by and for the consideration approved by the respective board of directors or managing member, as applicable, of each applicable Registrant;

(ix) in the case of Preferred Stock, the board of directors of Baker Hughes (the “Baker Hughes Board”) will have taken all necessary corporate action to approve the issuance and terms of the shares of the series of Preferred Stock, the terms of the offering thereof and related matters, including the adoption of a resolution establishing and designating the series of Preferred Stock and fixing and determining the preferences, limitations and relative rights thereof and the filing of a statement with respect to the series of Preferred Stock with the Secretary of State of the State of Delaware;

(x) in the case of Debt Securities, (a) any Parent Debt Securities will have been issued pursuant to the Parent Indenture and the Baker Hughes Board will have taken all necessary corporate action to designate and establish the terms of such series of Parent Debt Securities in accordance with the Parent Indenture, and such Parent Debt Securities will be governed by New York law and will not include any provision that is unenforceable, (b) the managing member of BHH LLC, and the board of directors of Co-Obligor (the “Co-Obligor Board”), if applicable, will have taken all necessary corporate or limited liability company action to designate and establish the terms of such series of Subsidiary Debt Securities in accordance with the terms of the Subsidiary Indenture or other applicable indenture, and such Subsidiary Debt Securities will be governed by New York law and will not include any provision that is unenforceable, (c) each of the Parent Indenture, the Subsidiary Indenture and any other indenture applicable to the Subsidiary Debt Securities will have become qualified under the Trust Indenture Act of 1939, as amended, (d) forms of Parent Debt Securities complying with the terms of the Parent Indenture, issued and evidencing such Parent Debt Securities will have been duly executed, authenticated, issued and delivered in accordance with the provisions of the Parent Indenture, and (e) forms of Subsidiary Debt Securities complying with the terms of the Subsidiary Indenture or other applicable indenture, issued and evidencing such Subsidiary Debt Securities will have been duly executed, authenticated, issued and delivered in accordance with the provisions of the Subsidiary Indenture or other applicable indenture;

(xi) in the case of Guarantees, (a) the Baker Hughes Board will have taken all necessary action to authorize and establish the terms of the Parent Guarantees and to authorize the terms of the offering and sale of such Parent Guarantees and related matters, and (b) the managing member of BHH LLC and the Co-Obligor Board, if applicable, will have taken all necessary action to authorize and establish the terms of the Subsidiary Guarantees and to authorize the terms of the offering and sale of such Subsidiary Guarantees and related matters;

(xii) in the case of Purchase Contracts, (a) the Baker Hughes Board will have taken all necessary corporate action to establish the terms thereof and approve the Purchase Contract Agreement relating thereto, (b) such Purchase Contracts will have been duly executed and delivered by Baker Hughes and the other parties thereto, and (c) such Purchase Contracts will be governed by New York law and will not include any provision that is unenforceable;

Baker Hughes Company

Baker Hughes Holdings LLC

Baker Hughes Co-Obligor, Inc.

December 1, 2023

Page 4

(xiii) in the case of Warrants, (a) the Baker Hughes Board will have taken all necessary corporate action to authorize the creation of and the terms of such Warrants and the issuance of the Securities to be issued pursuant thereto and to approve the warrant agreement relating thereto, (b) such warrant agreement will have been duly executed and delivered by Baker Hughes and the warrant agent thereunder appointed by Baker Hughes, (c) such Warrants and such warrant agreement will be governed by New York law, (d) neither such Warrants nor such warrant agreement will include any provision that is unenforceable, and (e) such Warrants or certificates representing such Warrants will have been duly executed, countersigned, registered and delivered in accordance with the provisions of such warrant agreement and the applicable Purchase Agreement to the purchasers thereof upon payment of the agreed-upon consideration therefor;

(xiv) in the case of Units, (a) the Baker Hughes Board will have taken all necessary corporate action to establish the terms of such Units and the terms of the Securities included in such Units, (b) the terms of the Units and the related Securities and their issuance and sale will have been duly established in conformity with the Purchase Agreement and any applicable contracts, agreements, indentures or other instruments that establish any component of the offered Units (including authorization of the issuance of any Securities to be issued pursuant to such Units), (c) each component of such Units will be authorized, validly issued, fully paid and nonassessable (to the extent applicable) and will constitute a valid and binding obligation of Baker Hughes or any third party (to the extent applicable) as contemplated by the Registration Statement and the Purchase Agreement establishing the Units, and (d) any Purchase Agreement establishing such Units or defining the rights of holders of such Units will be governed by New York law and will not contain any provision that is unenforceable;

(xv) all Securities and any related contracts, agreements, indentures and instruments will be duly executed and delivered in substantially the form reviewed by us prior to issuance of such Securities;

(xvi) the Securities offered, as well as the terms of each of the Purchase Agreements, or similar agreements with respect to any Securities offered, as they will be executed and delivered, do not result in a default under or breach of any agreement or instrument binding upon each applicable Registrant;

(xvii) each Registrant will have obtained any legally required consents, approvals, authorizations and other orders of the Commission and any other regulatory authorities necessary to issue and sell the Securities being offered and to execute and deliver each of the Purchase Agreements or similar agreements, as applicable; and

(xviii) the Securities offered, as well as the terms of each of the Purchase Agreements, or similar agreements with respect to any Securities offered, as they will be executed and delivered, comply with all requirements and restrictions, if any, applicable to each Registrant, whether imposed by any court or governmental or regulatory body having jurisdiction over such Registrant.

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 Class A common stock will, when issued, be legally issued, fully paid and nonassessable.

2. The shares of any series of Preferred Stock, will, when issued, be legally issued, fully paid and nonassessable.

Baker Hughes Company

Baker Hughes Holdings LLC

Baker Hughes Co-Obligor, Inc.

December 1, 2023

Page 5

3. The Debt Securities, Guarantees, Warrants, Purchase Contracts and Units included among the Securities will, when issued, constitute legal, valid and binding obligations of each applicable Registrant, enforceable against such Registrant in accordance with their respective terms.

The opinions set forth above are limited in all respects to matters of the internal law of the State of New York, the General Corporation Law of the State of Delaware, the Delaware Limited Liability Company Act and applicable federal law, each as currently in effect.

Our opinions expressed above are subject to the qualifications that we express no opinion as to the applicability of, compliance with, or effect of (i) any bankruptcy, insolvency, reorganization, fraudulent transfer, fraudulent conveyance, moratorium or other similar law or judicially developed doctrine in this area (such as substantive consolidation or equitable subordination) affecting the enforcement of creditors’ rights generally, (ii) general principles of equity (regardless of whether enforcement is considered in a proceeding in equity or at law), (iii) an implied covenant of good faith and fair dealing, (iv) public policy considerations which may limit the rights of parties to obtain certain remedies, (v) any requirement that a claim with respect to any security denominated in other than U.S. dollars (or a judgment denominated in other than U.S. dollars in respect of such claim) be converted into U.S. dollars at a rate of exchange prevailing on a date determined in accordance with applicable law, (vi) governmental authority to limit, delay or prohibit the making of payments outside of the United States or in a foreign currency or currency unit and (vii) any laws except the internal laws of the State of New York, the General Corporation Law of the State of Delaware. the Delaware Limited Liability Company Act and applicable federal law. We advise you that issues addressed by this letter may be governed in whole or in part by other laws, but we express no opinion as to whether any relevant difference exists between the laws upon which our opinions are based and any other laws which may actually govern.

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 Securities 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 sale of the Securities.

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 hereof and we assume no obligation to revise or supplement this opinion after the date of effectiveness should the internal laws of the State of New York, the General Corporation Law of the State of Delaware. the Delaware Limited Liability Company Act and applicable federal law be changed by legislative action, judicial decision or otherwise after the date hereof.

This opinion is furnished to you in connection with the filing of the Registration Statement in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act, and is not to be used, circulated, quoted or otherwise relied upon for any other purpose.

Baker Hughes Company

Baker Hughes Holdings LLC

Baker Hughes Co-Obligor, Inc.

December 1, 2023

Page 6

Sincerely,

/s/ Kirkland & Ellis LLP

Kirkland & Ellis LLP