I wouldn’t take your iMac G5 to the apple store, because they will most likely tell you to go to an Apple Specialist(depends on if it is under AppleCare or not)
What you can do is upgrade your RAM, when upgrading it, do it to the MAX! It will be a little more expensive now, but will last you a lot longer.
You can also upgrade the hard drive to a 7200 RPM drive, which will allow you to read and write faster.
Depending on your Processor, and RAM, you Can upgrade to leopard. But if you’re not more than 1ghz I don’t recommend it at all!
Like sndFreq said: If you’re under warranty, you HAVE to have the upgrades installed by an Apple Certified Technician. Or else you void your warranty and Apple will tell you to go away(Trust me I’ve seen it way to many times).
You can take it to a Apple Certified Repair Shop. You can use this website to find one near you:
http://www.applespecialist.com/
Good Luck!