If you open Kontakt 5 and click on the NI logo near the top right corner it will tell you which version you have. The last version was 5.8.1 (R43), you should be able to update to 5.8.1 from any older version of K5 for free. But you would have to buy an upgrade to get K6.
However, you should be able to load say, Otwin Campfire guitar by Johannes Menzel (8th day of Christmas offering). If that comes up as Demo, I think maybe you have reinstalled K5 but haven’t re-authorized it via Native Access.
btw, any purchased libraries might possibly need registering/authorizing via NI’s Native Access which should be on your desktop or they may say Demo on them.
See if you can figure out what’s happening, and if any of this info points to the issues you are having.