Did you uninstall while connected to the internet before you changed computers? That will free up an install seat. If you don't you will indeed run out of installations.
There is an alternative: deactivating. Go to your RL member page, select Registration, and then search for the entry for iClone 5:
Under Activated Number, the number of activations is listed. Click Details and a list of the activations is shown with computer names. Click Deactivate Now to free up an install seat.