To my knowledge there was never an OEM version of Lightroom. There are some camera manufacturers that supply LR with their cameras, Leica being one of them, but they aren't call OEM and you can't buy LR from these camera makers by itself.
So I don't know what you have and the only reasons I can think of you can't register it on the Adobe website is because it is some type of Pirated version or the serial number has been used before (you have a pirated serial number).
Whether the serial number you have for LR 5 will work as a qualified previous version to use the upgrade LR 6 I don't know. The only way to know is to buy LR 6 as the Upgrade version, install it, enter the LR 6 serial and when asked for a previous version serial number use that LR 5 serial number and see what happens. If it work you're OK. If it doesn't you can return LR 6 upgrade and buy the full version.