can I upgrade from 10.5.8 to 10.8.2 without data loss?

Data loss is not the issue. Having to upgrade your applications might be.

Start by checking if you can run Snow Leopard:

Requirements for OS X 10.6 'Snow Leopard'

http://support.apple.com/kb/SP575

OS 10.6 Snow Leopard is once again available for $19.99 from the Apple Store:

http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard

and in the UK:

http://store.apple.com/uk/product/MC573/mac-os-x-106-snow-leopard

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:

http://support.apple.com/kb/HT4759

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:

http://www.apple.com/osx/specs/

No, you are already on Leopard!

No. Please read my post!