1.Ke3 Kf5 2.Kf3 Kg5 3.Ke4 Kg6 4.Kf4 Kh5 5.Kf5 Kh6 6.Kg4 Wins

BOTH OPTIONS ARE WINNING

Yancey_Ward answer is correct
after 1.h4 rook cannot be saved
if 1...Rf3 2.Qxf3 Bxf3 3.hxg4
However 1.Kxg2 ?? is blunder…

last should be 4. not 3. But the the problem with site autosorting and editing defeciency

1. Bg6+ Kg7
   if 1...fxg6 2. Rxg6 Rg8 3. Qxh6#
2. Bh7+ Kxh7 3. Rh3 h5
   if 3... Rh8 4. Qxh6+ Kg8 5.Qxh8#
3. Rxh5+ Kg8 5.…

1.Rg4+ Kxg4 2.Ne3+ Kh4 3.Nf5+ Kg4 4.f3#

If black has to move first then it seems a draw

KarthikM !!

1. Be5+ Bxe5 2. Nf5+ Qxf5 3. Rd5+ Bxd5 4. Nb5+ axb5 5. c3# forced

Excellent AnupJ

or

4,Rd8+ Kc7
5.Ne6#