IF you go to your system settings and PSP information, it will show you usually....
5.50GEN or 5.00M33 or 5.03 ChikenHen.
if it's 5.03 chickenhen it is semi-hackable, this means it you to constantly reload the software (you'd know if you have this kind of psp, which is newer psp2000 and psp3000 devices).
there are no true hardmods for psps.
If it's 5.00 yes you can totally upgrade. I can give you a tutorial page if you want it. PM me. You'll be on 5.50GEND3 Final. which runs everything, but make sure you "run" games that have been patched.
Wynd