I own a copy of lightroom 5 (a download copy) and have had to install a new hard disk. I can't remember how I got the current copy but I think I may have downloaded a monthly rental copy because the program is asking me to pay a subscription fee. I was expecting to get a message to install my serial numbers.
You downloaded the trial version for the creative cloud. It doesn't work with a serial number. It is licensed differently. You will have to uninstall it and then download and install from here:
Thanks for your help, the link was very valuable to me...all is well in my world now.