I had a purchased an upgrade to lightroom 5 back in Dec and last week it disabled my use of develop module saying my trial has expired. On my account it says I purchased the upgrade and have a serial number. It is not giving me an option to enter serial number anywhere.
There are two licensing models for LR. If you have a serial number but your LR doesn’t have a place to ender a serial number, then you need to uninstall the cloud version of LR that you’ve apparently installed, and then download and install from the latest serial-number-activated LR 5.7.1 link near the top of the Adobe Updates page: