When data does not change, you cannot use triggers to do something with it. (Well you could create a trigger that does wildly inappropriate things on a table that changes, but I'd advise very strongly against it).
Create a script that does what you want (select employees, save to file, run delete query for the exact employees you have saved, NOT the employees from 5 years ago after you've finished, as it can be that some records just overstepped the mark between selecting them & saving them to file).
Run this every N time, N being the reasonable amount you may overstep the 'after exactly one year' mark (depending on circumstances daily, weekly or monthly most likely). Schedule that as a cron on the server, and do check up on it once in while to confirm it is still working.