Just to confirm:
You've followed these steps?
Which version is shown in the splash screen when you launch Lightroom: CC or 6?
Looks like the boxed version of Lightroom that the LCS sold me was Lightroom 5.
I followed those same procedures, but it didn't work.
I think you have installed the creative cloud version. You can still use Lightroom 5, but you need to download from the following website and activate it with the serial number that you have. You will have to uninstall the version you are trying to run now.
What James said.
Sounds like you've inadvertently downloaded the Lightroom trial version (which is version 6/CC) then tried to enter your Lightroom 5 serial number. Won't work so Lightroom remains in trial mode.
Uninstall then download LR 5.7.1 from the link provided above then enter your LR5 serial number.
Thanks Jim. I'll try that as soon as I get home to my DVD with it's serial number.