You are up to date as far as OSX 10.5 goes. Now you need to upgrade.
Software update, upgrade--what's the difference? - http://support.apple.com/kb/HT1444
You can upgrade to Snow Leopard, but check system requirements first:
Snow Leopard 10.6 Technical Requirements - http://support.apple.com/kb/SP575
You can buy Snow Leopard at:
Snow Leopard disc source - http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard
After installing run the updater to 10.6.8, then upgrade iTunes.
Jan. 2014 post by Kappy on doing all this: https://discussions.apple.com/message/24599931