My parents have a Mac Mini with Power PC G4 can it be upgraded to OS X 10.5 from 10.4?

Hello people,

My parents have a Mac Mini with Power PC G4 processor running OS X 10.4.11. I picked up a used printer HP Officeje 4620 and it seems as though it will work with OS X 10.5 or later. Can this Mini be upgraded and run OS X 10.5? Or do you know of an old printer that will run on this system?