The normal LR that is activated by a serial number and not some special cheap version like the student version shouldn’t expire, but at some point if you get a new computer with a different sort of operating system it may not run on it, anymore.
If you bought some sort of student version or a cloud-licensed version then it could expire.
Your boxed version was probably 5.0 and since its release there have been seven free updates. If you haven't been updating you should now update it to 5.7.1.
LR 5 is now nearing the end of its life and it is unlikely that any new updates will be issued, however it will continue to function fully forever, as long as it is on an appropriate computer. When LR 6 is released you will be able to purchase it at an upgrade price instead of the full cost, if you so wish.