Serial numbers come with the version you bought. If originally bought on disc with box it is on the packaging (Box). If originally bought as a download it was emailed to you. If originally bought as a download and directly from Adobe then the serial number "Should" be recorded on your Adobe ID account (email address and password you used when you originally bought it).
If you bought an Upgrade version you will also need the serial number from a previous version when you start LR 5 for the first time.
As for the download look here.