Sounds like you have the Creative Cloud version installed and you want the stand alone version if you have a serial. First of all you need to uninstall the creative cloud version, log out of the creative cloud and install the stand-alone version.
Download Links for Lightroom 5.7.1
If there is time left on the trial, a window should open when you launch the program asking if you want to continue the trial or to register. If the trial has finished it will only ask for a registration key. If LR opens normally without the window, go to Help/Lightroom Registration and put in the 24 digit key. I would recommend also opting for sending the info to Adobe to create an account and record the number there.
The above is predicated on the assumption that you have been using the perpetual license version of LR 5.7.1 and not by mistake the cloud subscription version (there has been a lot of confusion since Adobe started selling the two versions). If there is any doubt, uninstall the version you have now and do a new installation from here: