BAKER HUGHES a GE (BHI) 8-K Creation of a Direct Financial Obligation or an Obligation under an Off-Balance Sheet Arrangement of a Registrant

Exhibits 5.1 and 23.1

OPINION OF DAVIS POLK & WARDWELL LLP

May 1, 2020

Baker Hughes Holdings LLC

Baker HughesCo-Obligor, Inc.

17021 Aldine Westfield Road

Houston, Texas 77073

Ladies and Gentlemen:

Baker Hughes Holdings LLC, a Delaware limited liability company (the “Company”) and Baker HughesCo-Obligor, Inc., a Delaware Corporation (the“Co-Obligor, together with the Company, the “Issuers”) have filed with the Securities and Exchange Commission a Registration Statement on FormS-3 (FileNo. 333-222111) (the “Registration Statement”) for the purpose of registering under the Securities Act of 1933, as amended (the “Securities Act”), certain securities, including $500,000,000 aggregate principal amount of 4.486% Senior Notes due 2030 of the Company, for which theCo-Obligor is aco-obligor (the “Securities”). The Securities are to be issued pursuant to the provisions of the Indenture dated as of October 28, 2008 between the Company (as successor to Baker Hughes Incorporated) 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 as of July 3, 2017, among the Company, theCo-Obligor and the Trustee and as further amended and supplemented by the Fifth Supplemental Indenture, dated as of the date hereof, among the Company, theCo-Obligor and the Trustee (together, the “Indenture”). The Securities are to be sold pursuant to the Underwriting Agreement dated April 28, 2020 (the “Underwriting Agreement”) among the Issuers and the several underwriters named therein (the “Underwriters”).

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 Issuers that we reviewed were and are accurate and (vi) all representations made by the Issuers as to matters of fact in the documents that we reviewed were and are accurate.

Based upon the foregoing, and subject to the additional assumptions and qualifications set forth below, we advise you that, in our opinion, assuming the Securities have been duly executed and authenticated in accordance with the provisions of the Indenture and delivered to and paid for by the Underwriters pursuant to the Underwriting Agreement, the Securities will constitute valid and binding obligations of each Issuer, enforceable in accordance with their terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights generally, concepts of reasonableness and equitable principles of general applicability or the validity, legally binding effect or enforceability of any provision that permits holders to collect any portion of stated principal amount upon acceleration of the Debt Securities to the extent determined to constitute unearned interest.

In addition, we have assumed that the Indenture and the Securities (collectively, the “Documents”) are valid, binding and enforceable agreements of each party thereto (other than as expressly covered above in respect of the Issuers). We have also assumed that the execution, delivery and performance by each party to each Document to which it is a party (a) are within its corporate powers, (b) do not contravene, or constitute a default under, the certificate of incorporation or bylaws or other constitutive documents of such party, (c) require no action by or in respect of, or filing with, any governmental body, agency or official and (d) do not contravene, or constitute a default under, any provision of applicable law or regulation or any judgment, injunction, order or decree or any agreement or other instrument binding upon such party, provided that we make no such assumption to the extent that we have specifically opined as to such matters with respect to the Issuers.

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, General Corporation Law of the State of Delaware and the Delaware Limited Liability Company Act, except that we express no opinion as to any law, rule or regulation that is applicable to the Issuers, the Documents or such transactions solely because such law, rule or regulation is part of a regulatory regime applicable to any party to any of the Documents or any of its affiliates due to the specific assets or business of such party or such affiliate.

We hereby consent to the filing of this opinion as an exhibit to a report on Form8-K to be filed by the Issuers on the date hereof and its incorporation by reference into the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the prospectus supplement which is a part of 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