if I've purchased a full license of Prism 5, do I need to uninstall the demo version?

With Prism 5 for Windows, the installer uses the same program directory as a default and the full program replaces the demo, so there's no need to uninstall the demo unless you specify another directory when you install the full program. If you do, you can simply delete the folder with the demo so you won't get confused about which to use. It is not required.

With Prism 5 for Mac, the installer puts the full program in a different application folder, so both the demo and full version will be on your computer. If you've got a full Prism 5 license, it's probably a good idea to delete the folder Prism 5 Trial so you don't get confused about which program to use, but it's not required.