You got a serial number with the original purchase of LR 5. Whether you bought it in a retail package, box, or as a downloaded LR5 came with a serial number. If bought it in a box the serial number is on the box if you downloaded it you got an email with the serial number. If you bought it directly from Adobe then the serial # will be listed on your Adobe ID account.
In any event you will need that serial number and you can download the most current version of LR 5 (5.7.1) from the Adobe product Update website.