Your Adobe serial number has expired or is invalid

I recently purchased a new laptop to replace my previous which is over five years old. I am now going through my apps to ensure that I have transferred them ok, and, although I used Adobe Premiere successfully at the end of last week, on the new computer, when I tried using it just now I received the message that 'Your Adobe serial number has expired or is invalid'.

I postedthis info on the Adobe Support line, and after checking my serial number was told that I needed to re-install the software using the download link provided.  This I did, re-installed the software and re-loaded it only now to be informed that 'The serial number is already in use by the maximum allowed computers. You need to deactivate another computer to use this product'.

I've powered up my old laptop and loaded Premiere but can't see anywhere where I can deactivate it.  Can anyone help me?