Filed Pursuant to Rule 424(b)(5)
Registration No. 333-279588

PROSPECTUS SUPPLEMENT

(To Prospectus dated May 28, 2024 and

Prospectus Supplement dated May 28, 2024)

$5,239,073

Common Stock

This prospectus supplement amends and supplements the information in the prospectus supplement, dated May 28, 2024 (“Prospectus Supplement No. 1”), relating to the offer and sale of up to $5,239,073 of our shares of Common Stock, $0.0001 par value per share (“Common Stock”), pursuant to the Sales Agreement dated as of May 21, 2024 (the “Sales Agreement”) we entered into with A.G.P./Alliance Global Partners (“A.G.P.”). This prospectus supplement is registering the offer and sales of up to $5,239,073 of our shares of Common Stock from time to time through the Sales Agent, acting as agent. This prospectus supplement should be read in conjunction with Prospectus Supplement No. 1, and is qualified by reference thereto, except to the extent that the information herein amends or supersedes the information contained in Prospectus Supplement No. 1. This prospectus supplement is not complete without and may only be delivered or utilized in connection with, Prospectus Supplement No. 1, the accompanying base prospectus, and any future amendments or supplements thereto.

Our Common Stock is listed on The Nasdaq Capital Market under the symbol “PCSA.” As of July 22, 2025, the last reported sales price of our Common Stock on Nasdaq was $0.2497.

The aggregate market value of our outstanding shares of our Common Stock held by non-affiliates as of July 22, 2025, is $15,875,978, based on 40,284,356 shares of our Common Stock outstanding, of which 39,689,944 are held by non-affiliates, and a closing price on Nasdaq of $0.40 on June 11, 2025, which is within 60 days of the date of this prospectus supplement. Upon any sale of shares of our Common Stock under this prospectus supplement pursuant to General Instruction I.B.6. of Form S-3, in no event will we sell shares pursuant to this prospectus supplement having a value exceeding more than one-third of our public float in any 12-month period so long as our public float remains below $75,000,000.

As of the date of this prospectus supplement, we have offered and sold $1,546,338 of securities pursuant to General Instruction I.B.6 of Form S-3 during the 12-calendar month period that ends on and includes the date hereof, and therefore $3,692,735 is available to be sold pursuant to this prospectus supplement.

Investing in our shares of our Common Stock involves a high degree of risk and uncertainty. See “Risk Factors” beginning on page S-5 of Prospectus Supplement No. 1 and the other documents that are incorporated by reference in Prospectus Supplement No. 1 and the accompanying base prospectus.

NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR PASSED UPON THE ADEQUACY OR ACCURACY OF THIS PROSPECTUS SUPPLEMENT, THE PRIOR PROSPECTUS SUPPLEMENT OR THE ACCOMPANYING PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.

A.G.P.

The date of this prospectus supplement is July 25, 2025.