If you are indeed runnning 10.5.8 as your profile suggests then iTunes 10.6.3 is as high as you can go with Leopard OS. You have to upgrade to OSX 10.6.8 to run the newest iTunes. This involves purchasing a Snow Leopard disc from Apple (online or phone, not in stores).
Snow Leopard 10.6 Technical Requirements - http://support.apple.com/kb/SP575
Snow Leopard disc source - http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard