Finding dates in a column

The dates in column D and F are in the workbook.

Based on the Month (and year) in F13 I need to construct a formula to find:

1/ the last date in May in column D, which is 27/5 (D12)
and
2/ the last date the month before May, which is shown in column D, and which is 29/4 (D8).

How do we construct these two formulas ?

Please see the enclosed workbook.