Your computer's operating system is up to date as far as it goes, it just isn't high enough to meet the requirements of the newest iTunes. You need to upgrade.
Software update, upgrade--what's the difference? - http://support.apple.com/kb/HT1444
Get more information about your computer. Go to the Apple in the upper left corner of any window, then "About This Mac". Write down what it says about "version"and report that here. Now continue to "More Info..." Copy and paste the information here, but omit the serial number and Hardware UUID (if present).
You have an Intel Mac and 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
Here is the info you wanted, I assume I still need to upgrade to Snow Leopard? Which is just fine, happy to do it if that's the easiest and most cost affective 'fix'. Thanks for the help, btw.
Version: Mac OS X 10.5.8
Model Name: iMac
Model Identifier: iMac9,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.66 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 6 MB
Memory: 4 GB
Bus Speed: 1.07 GHz
Boot ROM Version: IM91.008D.B08
SMC Version (system): 1.44f0
For $20 it is pretty cost effective. You're clear for Snow Leopard as far as hardware goes. In the long term you could possibly (browse the tabs at the top of this page for Mavericks and supported machines) even go to the current (free) system Mavericks (10.9), but a step at a time. One issue with doing a big jump from 10.5.8 to 10.9 is you may find old software no longer works, so do some research first before you go that far. Snow Leopard lets you run old PPC generation software too but you have to install Rosetta which is on the installer disc.