Will my Arduino output pin at 0v handle 25 LEDs cathodes
I think you just answered your own question.   If you want to power 25 LEDs @ 20mA that's 500mA total.   So no you can't drive or sink 500mA with a single pin when that pin can only supply 40mA.   Try using a transistor on the output that can handle the current.  I think you're on the right track there.

Maybe try something like this.  Disclaimer though I only thought about that circuit for a few minutes, I didn't try it or sim it.   But that's half the fun :)