You are as up-to-date as you can be, given that you are using a very old version of Mac OS X that Apple no longer releases updates for. 10.5.8 is the most up-to-date version of 10.5 that is available. To get a newer system, you would have to purchase 10.6, 10.7 or 10.8.
So this is definitely not caused by malware of any kind. However, the fact that you are using such an outdated system does put you at higher risk of being infected with malware, so you should be sure to be extra cautious. See my Mac Malware Guide.
Start by checking if you can run Snow Leopard:
Requirements for OS X 10.6 'Snow Leopard'
The OS 10.6 Snow Leopard install DVD is available for $19.99 from the Apple Store:
and in the UK:
but nobody knows for how long it will be available.
When you have installed it, run Software Update to download and install the latest updates for Snow Leopard to bring it up to 10.6.8, or download the combo update from here:
Check via Software Update whether further updates are required.
You should now see the App Store icon in iTunes, and you now need to set up your account:
To use iCloud you have to upgrade at least to Lion, but some functions are only available in Mountain Lion:
You can also purchase the code to use to download Lion (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard), or you can purchase Mountain Lion from the App Store - if you can run that:
Snow Leopard (10.6) is certainly the oldest version of Mac OS X still receiving security updates. It doesn't have all the security enhancements that are present in the latest system, but it's still pretty secure overall. Leopard is less so.
If your machine is capable of running Snow Leopard, I'd certainly consider Klaus' suggestion of upgrading to be an excellent one.
Only if the Snow Leopard DVD is the white retail one with the Snow Leopard logo, and your wife no longer has Snow Leopard installed on her machine. If she bought a Snow Leopard family pack, and you are in the same household, you can use that without worry of license violation even if she does have it installed. If it is Mac model labelled on it, you can't use it on your MacBook Pro.