Per record retention for the agency, I need to delete timesheets past 5 years old.
There is a job called "Delete Investments and Time Reporting Periods Job", you can mark Time Periods for Deletion by going to Administration->Time Reporting Periods and run the job which will delete them and any associated timesheets for those periods. So basically you can mark any time periods that are 5 years or longer and then you run the job. I would suggest you try this in non production environment first and see how it goes and whether it satisfy your retention requirement.
Note: When running a job don't check the "Delete Marked Investments with Timesheet and Transaction Data" because you are only after timesheet data.
Documentation link here