create a function (which accepts person's ID) and returns total number of personal days (that would be a simple SELECT statement with a SUM function) and - probably - a WHERE clause that restricts rows to ... what? The last year?
on Apex page, create a validation for item you use to enter number of personal days; its type would be a PL/SQL Function which returns error text, and checks whether number of entered personal days + total number of personal days (so far) (returned by a function) exceeds 5 days. If so, display an error.