Have you registered Lightroom 5 at all?? It doesn't sound like it... Look in the Help Menu...
How did you purchase LR 5? If it was from a DVD disc then you have the packaging that contains the serial number.
If it was bought as a download, IE no DVD disc, then you received the serial number in an email and in that case you should of recorded the serial number in a text or word processing document and SAVED that email for safe keeping.
Never count on Adobe to keep the serial numbers for the software you bought. IMHO that is your responsibility.
If it was part of the Photographers subscription package that includes both LR and PS you use the Creative Cloud desktop app to reinstall.
The serial number for your current install can be found on your hard drive. Search for this file "Lightroom 5.0 Registration.lrreg" in windows and this file on a Mac Lightroom 5.0 Registration
Make a HARD copy of it and put it in a safe place.
If you have registered it the serial number will be with Adobe.
If you have it installed on your computer you can also recover the serial number from your operating system.
Quote "Try using Windows Explorer to go find on your system drive ProgramData>Adobe>Lightroom and in there you should see the file "Lightroom 5.0". Open that file with Notepad or any other text editor and you should see your full serial number."
You should be able to see and copy the serial number for your current installed application
Right you are. I had not registered it. I don't remember registering the other versions that do show up on Adobe, but 5.0 may had been purchased through a Kelby special or something.
Great Gary, you can just d/load and install the current version (Lr5.7.1 - making sure not to get the CC licensed version) and use the serial number you have. Don't for get if you have an upgrade serial number you will be asked for the Lr4 serial number as well....
if you search for the files I posted both serial numbers will be in that file. The V5 serial and the older version you used to qualify for the upgrade to V5.