White to play and win
In order to win, white needs to promote one of their pawns. Taking on c7 won't work, so white needs to find a different idea.
1.Rg5!!
This move deflects the black rook from d5 in order to promote a pawn.
1...Rxg5 2.c6!
This was the idea behind 1.Rg5
2...Rh5+ (2...cxd6 3.cxd7 and white promotes) 3.Kg7!
3.Kg6?? This move actually loses: 3...dxc6 4. dxc7 (4. Kxh5 cxd6) 4...Rh8 -+
This is the reason why the white king needs to go to g7: the black rook cannot be allowed to
reach the 8th rank
3...Rg5+ 4.Kf7 Rf5+ 5.Ke7
Black to play
5...dxc6
5...Re5+ 6.Kxd7 cxd6 7.b4! (Taking the c5-square under control) (7.c7? Rc5 8.b4 Rxc7+ 9.Kxc7 d5 =) 7...Rb5 8.c7 Rxb4 9.c8=Q And this is a win for white
6.dxc7 Re5+ 7.Kd7 Rd5+ 8.Ke6! And white will promote and win. 8. Ke7 (This move also wins because white can repeat the position) 8...Re5+ 9.Kd7 Rd5+ 10.Ke6