enjoy the puzzle and plz notify me if there is a faster and quicker mate

Good puzzle, I think that is the fasted way to mate.

nice!

You need to tell us what happens exactly after 1.Rd8+ Kf7.

i think after 1.Rd8+KF7.  BLACKS BEEN MATED MORE QUICKLY BY QH5+, FORCED MOVE FOR BLACK KE6 THEN ROOK CHECK AND BISHOP COMES IN THE MIDDLE AND RxB THEN Qe4,RxQ and mate.

After 1.Rd8+ Kf7 2. Qh5+ the reply 2...g6 makes it impossible for White to get a mate in 5 moves.  Most likely it would take White not 5 but 13 moves to get a mate:

3.Qh7+ Ke6 4.Re1+ Be2 5.Rxe2+ Kf5 when White would need 8 more moves to get a mate:

6.Rf2+ Kg5 7.h4+ Kg5 8.Qxg6+ Kh3 9.Qf5+ Qg4 10.Rh2+ Kxh2 11.Qxg4 and only now is a mate clear: 11...Rxa2 12.Rd2+ Kg1 13.Qd1#