Okay, you need to find a file called reaper-license.rk. This would have originally came in an email when you purchased Reaper and after registering the license in Reaper it would have been located either in the Reaper program folder (where the Reaper.exe file is located) or in the Reaper 'data' folder in the Reaper 'AppData' folder.
A Reaper license is good for two full versions... so if you bought your license in Reaper 3, you need a new license. If you bought your license in Reaper 4 then you're good till Reaper 6, which is quite a ways off as Reaper 5 was just released.
Good luck!