Vacation Entitlement based on full years of service and odd vacation year

Maybe something like:

=IF(start_date - DATE(2017, 5, 1)>395, INDEX({10,15,20,25}, MATCH((start_date - DATE(2017, 5, 1)) /365.25, {1,4,10,18}, 1)) , MIN( INT((start_date - DATE(2017, 5, 1)) /30), 10))

"start_date" to be changed to the appropriate cell reference for the given employee's start date.

And that DATE(2017, 5, 1) thing might need to be changed to either a reference to another cell referencing the start date of the fiscal year (if you have one), or maybe a test that updates it to the most recent May 1st, using an IF buried in there.

Also that's going off "30 days", not "1 month" -- it's a little different than what exactly you asked for, but fiddling with count of full months is a lot more complex.

And you might want to feed the lookup with a table, instead of having arrays embedded in the formula. More stable that way.