How quickly can you find the shortest mate in this position? I found the first move eay, but it was harder after that.

Q7/1K6/R7/8/4P3/8/6pp/7k w - - 0 1

V-11.e5 Kg12.Qa7+ Kf13.Ra2 g1=Q4.Qa6+ Ke15.Qe2#

V-21.e5 Kg12.Qa7+ Kh13.Qe3 g1=Q4.Qf3+ Qg25.Ra1#

V-31.e5 g1=Q2.Kc7+ Qg23.Ra1#

V-41.e5 Kg12.Qa7+ Kh13.Qe3 g1=N4.Rg6 any move5.Qf3#

I think it isn't the shortest mate. I will think further.

At last I guessed how to mate in 3.

V-11.Qf8 g1=Q2.Qf3+ Qg23.Ra1#

V-21.Qf8 g1=N2.Rg6! Ne23.Qf3#

V-1

1.e5 Kg1

2.Qa7+ Kf1

3.Ra2 g1=Q

4.Qa6+ Ke1

5.Qe2#

V-2

1.e5 Kg1

2.Qa7+ Kh1

3.Qe3 g1=Q

4.Qf3+ Qg2

5.Ra1#

V-3

1.e5 g1=Q

2.Kc7+ Qg2

3.Ra1#

V-4

1.e5 Kg1

2.Qa7+ Kh1

3.Qe3 g1=N

4.Rg6 any move

5.Qf3#

I think it isn't the shortest mate. I will think further.