Exhibit 5.1

[ZGBC Letterhead]

August 2, 2016

Spherix Incorporated

1350 Avenue of the Americas, 2^nd Floor

New York, New York 10019

Ladies and Gentlemen:

You have requested our opinion, as special counsel to Spherix Incorporated, a Delaware corporation (the “Company”), with respect to certain matters in connection with the offering by the Company of up to 1,592,357 shares of its common stock, par value $0.0001 (the “Shares”) pursuant to the Registration Statement on Form S-3 (No. 333-198498) (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933 (the “Act”), the prospectus included within the Registration Statement dated November 10, 2014 (the “Base Prospectus”), and the prospectus supplement dated August 2, 2016, filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations of the Act (the “Prospectus Supplement”). (The Base Prospectus and Prospectus Supplement are collectively referred to as the “Prospectus.”) The Shares are to be sold by the Company as described in the Registration Statement and the Prospectus.

We have examined and relied upon the Registration Statement and the Prospectus, the Company’s Certificate of Incorporation and By-laws, as currently in effect, and the originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as we have deemed relevant in connection with this opinion. We have assumed the genuineness and 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.

We are licensed to practice in the State of New York. This opinion letter is limited to New York law, the Delaware General Corporation Law and applicable federal law of the United States. We are not rendering any opinion as to compliance with any federal or state antifraud law, rule or regulation relating to securities or to the sale or issuance thereof.

On the basis of the foregoing, and in reliance thereon, and subject to the qualifications herein stated, we are of the opinion that the Shares, when sold in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and non-assessable.

We 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 a Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement.