I am reinstalling the old version of Indesign CS5 on a new laptop. It activates but I get an error.

Consider yourself very lucky.

Registering is a different thing altogether. That is a mechanism for Adobe to know you have that version/serial associated with your account. If you had previously registered it in the past, it should still show on your Adobe Accounts page under Plans and Payment > Products (my screen grab shows my old CS5.5 Suite still registerd from 2011); you won't need to register it again. 

If it doesn't show, or you never registered before, you could try register it now by entering the serial number. How successful that will be in 2025 I can't say. It's been awhilllle.

If it works at all just be thankful. CS5 was released about 15 years ago. As for activation, if you still have the old machine make sure you deactivate it there.