Hello, my name is Joan Fluvia.
I was a chess player and a friend show me your website to solve the chess problems.
I found them very interesting but I have a doubt.
There is the solutions I found:

4... Qb5#  1.d4 e5 2.Kd2 Qg5+ 3.Kc3 exd4+ 4.Kb3 Qb5 #
5.Ng3#  1.e3 e6 2.Qg4 Ke7 3. Ne2 Kf6 4. Qxg7+ Kf5 5.Ng3#
5.Qxe4#  1.d4 e5 2.Qd3 Ke7 3.Bg5+ Ke6 4.Be7 e4 5.Qxe4#
5... Rh1#  1.g4 h5 2. Bg2 hxg4 3. Bxb7 Rxh2 4.Nh3 Bxb7 5.0-0 Rh1#
6.Nd3#  1.Nf3 e6 2.Ne5 Ke7 3.Nc3 Kf6 4.e4 Kg5 5.Qh5+ Kf4 6.Nd3#
6.gxf8=N# 1.h4 d5 2.h5 Nd7 3.h6 Ndf6 4.hxg7 Kd7 5.Rh6 Ne8 6.gxf8=N#

All of them seems to be unique solutions less the 6.Nd3#.
Is easy to see that white can change the order of the moves, or black can play e5 instead of e6 or play f5 Kf7 Kf6 Kg5 Kf4 (if white plays Ne5 in third movement)
I think there is a tipo error. It can be maybe 6.Ne3#?

Thanks,

Joan Fluvia
-----------------------------------------------------------