Was shooting my 627-5 yesterday and had two misfires on a new cylinder. Turned out to be a broken firing pin. I requested a call tag from S&W but I'm wondering if I should just change it myself? Any thoughts are welcome.

I personally wouldn't send the gun back for something like this, especially if you are familiar with the procedure in terms of properly removing the sideplate. Replacement pins are available from several different vendors, and from the factory. Very easy to replace this particular part.

If you decide to repair/replace the pin yourself, be sure to clean the firing pin cavity in the frame with Gun Scrubber or similar on a Q-tip. You want to remove all the traces of fouling and debris, and then leave the cavity, and the new pin and spring dry (un-lubricated) when they are re-installed.

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Ret. LE, FA Instr, S&W Armorer

If you are comfortable removing the sideplate, it will be quicker if you order a firing pin or an extended firing pin and install it.
The factory just told me that they are really backed up right now. And said it'd be 6 more weeks on top of what my gun had already spent there.

Colt told a customer that it would be 6-8 weeks to replace a broken V spring in a New Cobra.

If they are going to send out junk, they need to hire more warranty clerks.

That's what I've been thinking. I have a stock firing pin out of my 625 and a new Apex in stock.