I recently had to reinstall my Mac OSX 10.4.11 due to some software problems and lost most of my applications. When trying to re-download Skype, the version provided at their sight was only for Mac OSX 10.5 or higher. Messenger for Mac 7.0.3 makes it easy to take advantage of the full power of real-time communications. Messenger service has been shut down by Microsoft, with users being directed to change to the Skype network. Mirror download will remain for completeness. System Requirements: Mac OS X 10.4.9 or later.

You need some more RAM, but:

Start by checking if you can run Snow Leopard:

Requirements for OS X 10.6 'Snow Leopard'

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

Download Skype App On Mac

and in the UK:

but nobody knows for how long it will be available.

To use iCloud you have to upgrade all the way to 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:

Mac 10.4 Upgrade

Mac 10.4 Tiger

When you have installed it, run Software Update to download and install the latest updates for Snow Leopard.