Same version of Lightroom on the Mac and PC? Both versions are running Lightroom 5?
Do you have any records anywhere of your Lightroom serial number? Did you save the CD and box it came in, or if you downloaded it, did you save the e-mail that provided the serial number? (... and if not, maybe you might want to consider developing a method to save your serial number for all software ... just a little friendly advice ...)
If you registered your product with Adobe, you should be able to log in to the Adobe web site and obtain your serial number there.
And if that doesn't work ... I dunno
Yes, same LR version on Mac and PC.
I grabbed the full Serial number from the Mac install. I recall doing this SAME thing (cut/paste) when I initially installed on LR5 on the PC Laptop the first time.
I'm wondering if I needed to "deactivate" from the PC Laptop (install #2) before reformatting... Though I do see some random posts that indicate deactivation is not needed on LR5.
No deactivation needed ... so are you implying you have no records of the actual serial number? In that case, you would need to log on to your Adobe account and obtain your serial number from there assuming you registered it with Adobe.