First make sure your OS is up to-date, then go to Adobe's website and download the newest Flash Player for your OS and install it,(a G5 is non intel mac, thats why you couldn't install latest player from adobe) Mac OSX 10.4xxx or 10.5xxx for a G5, Mac OSX 10.6 only runs on Intel.
Edit; You need flash player 10.1; http://fpdownload.macromedia.com/get/flashplayer/installers/archive/fp10.1_archive.zip
10.2 and higher requires Intel Mac.
First make sure your OS is up to-date, then go to Adobe's website and download the newest Flash Player for your OS and install it,(a G5 is non intel mac, thats why you couldn't install latest player from adobe) Mac OSX 10.4xxx or 10.5xxx for a G5, Mac OSX 10.6 only runs on Intel.
Edit; You need flash player 10.1; http://fpdownload.macromedia.com/get/flashplayer/installers/archive/fp10.1_archive.zip
10.2 and higher requires Intel Mac.