I have LR5 as well as CC. Each allows use on two computers.
I'm not sure what you mean by Add-On, mine is a upgrade copy, if I remember. It was a download, so I only received the key from Adobe, and downloaded the software. I also had to enter the key from a previous version, even if it was also a upgrade version.
If you still have the key to yours, you can download it and use the key. I've been keeping my old versions, just in case I do away with CC. So far, CC is fine for me, and the price is right.