I have just downloaded LR5 as a new install on my new PC and when I input the registration it does not recognise it.
It states "the serial number is invalid" but it is exactly what was is on the email. It worked on my laptop.
From the sound of your question, it sounds like your first installation was a standalone version - is that correct? If so, did you download the new install from the CC part of Adobe; that would explain why your serial number didn't work, as the two versions are incompatible.
Thanks for the answer and it was spot on. Luckily I had the download version on my laptop and installed it and its up and running.