Mac OS X 10.5 Leopard was the last operating system to support the PPC Macintosh computers. 10.6 Snow Leopard dropped its support for PPC.
What you can do, if possible, is to instal Ubuntu (which is linux) on your Power Mac G5 and hopefully there are drivers that support your hardware. I never done it before, but i was thinking about it when i wanted to continue using my 1.2 GHz iBook G4. Instead i just gave it to my dad.
Not like a Mac is the short answer! Go for Leopard. I'm not convinced that the changes to OS X since then have all been improvements.
The only reason to go for newer versions of OS X (IMO) is if you want to do iPhone/iPad development as the latest versions of iOS need newer versions of OS X. Otherwise, Leopard is probably the best and fastest version of OS X.