There is no deactivation possible or needed with Lightroom.
The problem is your serial number, perhaps its for LR4 or earlier, perhaps you typed it in wrong, perhaps there's something else wrong.
Do you actually have a problem relicensing LR5 or are you just wondering what you need to do?
Download and install the LR 5.6 update from here: http://www.adobe.com/downloads/updates
Enter your LR 5 serial number and you should be all set. If something isn't working, then, please describe the problem in detail.
Your advice pushed me to reinstall.
I entered the licencing info from a popup that appeared after launching LR5 and just did what required. It worked just ok!
At first installation, I closed the popup with the idea to check my LR-Photo-archive in first step. Once I could check that all my pictures were ok, I entered manually the licence data from <help> + <LR registration>; registration steps and program behaviour were slightly different and were unsuccessful each time I tried.
I have to tell that my current LR5 licence is issued from upgrade from LR4... may be licence number required were first previous one or I entered the bad one...
Anyway, happy that recovery and reinstalling process ran properly.
Thank you again.