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i think calbob was just offering some friendly advice, id try not to be so quick to jump down his throat. He DOES know what hes talking about, because Apple's don't have a registry. So a file transfer is all youll need to do, you just need to find where the serial number pref is kept. Its in either your /~(Home)/Library/Peferences/ folder or knowing adobe, it might be in /~/Library/Application Support/Adobe/
All youll need to do is to search (command+f) for anything named "adobe" in your home library. Then just transfer that and the application over to the G5. My only warning is that this might be a little risky since the G5 runs on 10.2.7 and im guessing your G3 is on 10.2.6 or 10.2.8. There shouldnt be any real difference when it comes to running an app, but just kinda a disclaimer
Hope this helps