Shorted V5 pin to GND

I know it wasn't smart and I was rushing to do a test run. I shorted the V5 pin and the GND pin.
Is there any saving the the Arduino UNO?
I was using a 12 volt power supply plug into the power jack.
When the Arduino is powered up, the ON led and L led are lit and not flashing.
Nothing is recognized in the computor, USB working fine, I do have a backup Arduino and it is working fine.
I read some posts about changing the voltage regulator but having 12 volts at the V5 pin may be to much for everything to handle.
Was just wondering if its worth trying or not?
Thanks for your help

It's basically not worth it.

If you shorted the 5V pin while feeding with 12V on the barrel, the 5V regulator will probably not have survived it (although it has thermal protection).

I would remove the regulator and see after that if the board still works from USB.

If it has a DIP 328P, you might be able to use it in another Uno or in a "Arudino on a breadboard" style setup; just in case the processor is damaged (from your description, I'm not sure how that would have happened), I would prefer the latter.