Try below steps
Quit Lightroom 5
Hold windows key on your keyboard and Press R key.
In Run window type %programdata% and click on Ok
Open Adobe > Lightroom folders
Delete Lightroom5install cookie file.
Launch Lightroom 5 and check if you are getting the window to enter the serial number.
Also uninstalling Lightroom will not remove catalog from your computer, after re installation while launching it will detect your previous catalog.
You should just uninstall what you have installed for LR 5.x, now, then download and install the LR 5.6 update from the Adobe Updates page, and enter your standalone serial number, and things should pick up where you left off.
You might want to go into LR’s preferences (if LR is still opening for you) and see where the catalog (.lrcat) file actually resides on your computer in case you have a problem and have to double-click on that .lrcat file to open your catalog, but my experience is that nothing will seem different after you’ve installed the new version other than the version number will be newer. The preferences, catalog, and pictures are somewhere different than where the program is installed so uninstalling and reinstalling shouldn’t affect any of it.
LR 5.6 update is here: http://www.adobe.com/downloads/updates/
FYI, the CC-LR is licensed by logging into CC, the standalone version is licensed by entering a serial number. That is why you have to uninstall the CC_licensed version and install the non-CC-licensed version.
It also probably wouldn’t mess anything up to install LR 5.2 from the DVD, but then you’d have to turn around and immediately download the LR 5.6 update, anyway, and it would waste time, so why not start with the latest update. The update is a fully function program, not a patch to an existing program. It’ll either find your existing licensing information if you’ve already entered the serial number or ask for a serial number if it doesn’t find anything—which sounds like your situation.
That did it. I uninstalled the trial version (and Creative Cloud), installed the 5.6 full version from download, then entered the license key from the CD. My existing LR catalog was ready to use.
Wow, I don't know why LR software is so big. It takes forever to uninstall and install.
So my problem was that I had installed LR5 using the Creative Cloud trial, since that is the only way that Adobe makes visible for installing trial software. If I had started with the 5.6 full download, I would not have had to ask for help here. But I'll repeat that these community forums are really fantastic. Thank you all for prompt help!