Exhibit 5.1

Danaher Corporation

2200 Pennsylvania Avenue NW, Suite 800W

Washington, DC 20037-1701

2.400% Senior Notes due 2020

3.350% Senior Notes due 2025

4.375% Senior Notes due 2045

Ladies and Gentlemen:

We have acted as counsel for Danaher Corporation, a Delaware corporation (the “Company”), in connection with the issue and sale by the Company of $500,000,000 aggregate principal amount of its 1.650% Senior Notes due 2018 (the “2018 Notes”), $500,000,000 aggregate principal amount of its 2.400% Senior Notes due 2020 (the “2020 Notes”), $500,000,000 aggregate principal amount of its 3.350% Senior Notes due 2025 (the “2025 Notes”) and $500,000,000 aggregate principal amount of its 4.375% Senior Notes due 2045 (the “2045 Notes,” and together with the 2018 Notes, the 2020 Notes and the 2025 Notes, the “Notes”), pursuant to an underwriting agreement dated as of September 10, 2015 (the “Underwriting Agreement”) among the Company and Citigroup Global Markets Inc. and Barclays Capital Inc., as representatives of the several underwriters named therein. The Notes will be issued pursuant to an indenture (the “Base Indenture”) dated as of December 11, 2007 between the Company and The Bank of New York Mellon Trust Company, N.A. as trustee (the “Trustee”), as supplemented by a supplemental indenture (the “Supplemental Indenture” and together with the Base Indenture, the “Indenture”) of even date herewith between the Company and the Trustee.

The Company filed with the Securities and Exchange Commission (the “Commission”) a Registration Statement on Form S-3 (File No. 333-203948) under the Securities Act of 1933, as amended (the “Securities Act”), on May 7, 2015, and the Company and DH Europe Finance S.A., a Luxembourg public limited company, filed with the Commission a Post-Effective Amendment No. 1 to the Registration Statement on Form S-3 (File No. 333-203948) under the Securities Act, on June 15, 2015, including the prospectus dated June 15, 2015 (the “Base Prospectus”). The Company filed with the Commission the Base Prospectus, as supplemented by the preliminary prospectus supplement dated September 10, 2015 (the “Preliminary Prospectus Supplement”) on September 10, 2015, and the final prospectus supplement dated September 10, 2015 (the “Prospectus Supplement”) on September 11, 2015.

Wilmer Cutler Pickering Hale and Dorr LLP, 1875 Pennsylvania Avenue NW, Washington, DC 20006

Beijing    Berlin    Boston    Brussels    Denver     Frankfurt    London    Los Angeles    New York    Oxford    Palo Alto    Washington

Danaher Corporation.

September 15, 2015

Page 2

We have examined and relied upon corporate or other proceedings of the Company regarding the authorization of the execution and delivery of the Indenture, the Underwriting Agreement and the issuance of the Notes, the Registration Statement, the Base Prospectus, the Preliminary Prospectus Supplement, the Prospectus Supplement and the Indenture. We have also examined and relied upon originals or copies, certified or otherwise identified to our satisfaction, of such other corporate records of the Company, such other agreements and instruments, certificates of public officials, officers of the Company and other persons, and such other documents, instruments and certificates as we have deemed necessary as a basis for the opinions hereinafter expressed.

In our examination of the documents referred to above, we have assumed the genuineness of all signatures, the legal capacity of all individual signatories, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as copies, the authenticity of such original documents, and the completeness and accuracy of the corporate records of the Company provided to us by the Company.

In rendering the opinions set forth below, we have assumed (i) the due execution and delivery, pursuant to due authorization, of the Indenture by the Trustee; (ii) that the Trustee has all requisite power and authority to enter into and perform its obligations under the Indenture; and (iii) the Indenture will be a valid and binding obligation of the Trustee. We have also assumed that there will not have occurred, prior to the date of issuance of the Notes, any change in law affecting the validity or enforceability of such Notes and that at the time of the issuance and sale of the Notes, the Board of Directors of the Company (or any committee thereof or officer of the Company acting pursuant to authority properly delegated to such committee or officer by the Board of Directors) shall not have taken any action to rescind or otherwise reduce its prior authorization of the issuance of the Notes.

We express no opinion herein as to the laws of any jurisdiction other than the state laws of the State of New York, the General Corporation Law of the State of Delaware and the federal laws of the United States of America.

Our opinions below are qualified to the extent that they may be subject to or affected by (i) applicable bankruptcy, insolvency, reorganization, moratorium, usury, fraudulent conveyance or similar laws relating to or affecting the rights or remedies of creditors generally, (ii) duties and standards imposed on creditors and parties to contracts, including, without limitation, requirements of materiality, good faith, reasonableness and fair dealing, and (iii) general equitable principles. Furthermore, we express no opinion as to the availability of any equitable or specific remedy upon any breach of the Indenture or the Notes, or to the successful assertion of any equitable defenses, inasmuch as the availability of such remedies or the success of any equitable defenses may be subject to the discretion of a court. We also express no opinion herein with respect to compliance by the Company with the securities or “blue sky” laws of any state or other jurisdiction of the United States or of any foreign jurisdiction. In addition, we express no opinion and make no statement herein with respect to the antifraud laws of any jurisdiction.

Danaher Corporation.

September 15, 2015

Page 3

On the basis of, and subject to, the foregoing, we are of the opinion that when the Notes have been duly executed by the Company and when duly authenticated by the Trustee in accordance with the terms of the Indenture, and delivered to the purchasers thereof against payment of the consideration in accordance with the terms of the Underwriting Agreement therefor duly approved by the Company, the Notes will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms.

Please note that we are opining only as to the matters expressly set forth herein, and no opinion should be inferred as to any other matters. This opinion is based upon currently existing statutes, rules, regulations and judicial decisions and is rendered as of the date hereof, and we disclaim any obligation to advise you of any change in any of the foregoing sources of law or subsequent developments in law or changes in facts or circumstances that might affect any matters or opinions set forth herein.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Company’s Current Report on Form 8-K to be filed on or about September 15, 2015, which Form 8-K will be incorporated by reference into the Registration Statement and to the use of our name in the Preliminary Prospectus Supplement and Prospectus Supplement under the caption “Legal Matters.” In giving such consent, we do not hereby 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.