Go to the Adobe main web site. Scroll down to the bottom of the page and click the little link that says Products. Find Lightroom in the list and click on the BUY button. Change the Full to Upgrade by clicking on Full. Then select the version you are upgrading from. Put in your CC info and download LR 6. Adobe will ask you to either sign in with a current Adobe ID or create one. Create one if you don't already have one.
Then when the download of LR 6 finishes run the installer. It does not install over the top of LR 5. It installs to a separate folder. So you will still have access to LR 5 if you want to use it.
Once the install finished start the program. It will ask you "Do you want to Try, Buy or enter a serial number. You would select enter a serial number.
You will have to Sign In using your Adobe ID, the one you had or the one you created at time of purchase, then a page/window will come up where you enter the serial number.
Since you still have LR 5 installed it shouldn't ask you for a previous version serial number. It will then find your LR 5 catalog file, make a copy of it and covert that copy to a LR 6 catalog file. The LR 5 and LR 6 catalog files are not compatible. LR 6 will upgrade the LR 5 catalog but you can't use the LR 6 catalog file in LR 5.
Thank you for your help:-)