10.5.8 is the most up to date version of Leopard. Without details of your machine we cannot advise further.
Check out 'About this Mac' from the Apple menu above and tell us what it says about the processor and Memory. Then we can tell you how much higher you can upgrade.
If these details are in your profile, it would help the next time you ask questions.
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 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: