If you have 2 serial numbers for iClone 5 then you can have 1 copy on your old PC and 1 on the new PC - and still be able to install each on another 2 PCs if you want. Each license, Serial number, allows 2 installs - the restriction being that both can't be used at the same time.
You can have both iClone 5 and 6 on the same PC - it's a good thing to do until you are sure that all of your iClone 5 projects work without problems in iClone 6.
As for not being "purchased" - it doesn't matter if you paid for it, won it, or got it for free. If you have a legal serial number provided by Reallusion then you can install it and enjoy. :)
Gerry
System: Win 10 Pro (21H2), Asus X99-E WS, CPU i7-5930K -3,5 GHz, 32 GB DDR4 2666-16 RAM, NVidia GTX 1080 Ti GPU - 11 GB VRAM(Driver Studio-536.99), Samsung 850 Pro 512 GB SSD, 6 TB HD storage.