Should white be able to win this endgame? Should white be able to win from the position

[fen "8/5k2/3p1p2/3PnP2/1KP1r1P1/8/3RB3/8 b - - 0 67"]


with black to move?

(A game I was playing ended there when black just let

black's time run out due to having very little of it left.)

Black can take the g4 pawn, but Stockfish evaluates that as being much worse than

black's alternatives, regardless of whether the capture is immediate or after Ke7 Kb5.

Thus, play should presumably continue Ke7 Kb5 Nd7, resulting in the position

[fen "8/3nk3/3p1p2/1K1P1P2/2P1r1P1/8/3RB3/8 b - - 0 69"]


with white to move. ​ From that position, Bd1 is the only way Stockfish sees to make progress.



However, after Bd1, Stockfish thinks black should play Ne5, and then the line it gives is

4. c5 dxc5 ​ 5. d6+ Kd7 ​ 6. Kxc5 Nf7 ​ 7. Bc2 Re5+ ​ 8. Rd5 Rxd5+ ​ 9. Kxd5 Nxd6 ​ ​ ,

which results in a draw since

with white's pawn still on g4, Nf7 will establish a fortress because black can play Ke7 and N(x)g5 and even if white gives up the g4 pawn, white's king can't attack more than one of {h3,e4,h7}

and the only way for the bishop to do that is from g2, which leaves f7 safe for the knight

and

g5 fxg5 gives a tablebase draw, regardless of whether white plays that immediately

or after Ba4+ Ke7, and Ba4+ Ke7 Be8 Nxe8 gives a tablebase win for black
.



(Reminder: ​ My question was at the top of this post.)
White's main threat is c5, which forces a pawn exchange and a passed pawn with king covering queening squares. The bishop is covering the g pawn.

Should black force an exchange of that pawn, white's rook could go to e5 and capture the d pawn, allowing a double passed pawn.

If black defends c5, white first move his king to b4 to cover the next 2 pawn squares, then force black to zugzuang(by moving rook to a file) which forces black to stop defending c5 or move the rook. 

If black moves rook to e5, putting pressure on the bishop, white pins black's knight and therefore forces a minor piece exchange, with a more active king, which will then go on and promote pawns. 

If black stops pressuring the bishop, the endgame should be easily winnable.

As for Ke7, idea would be the same

For moves that does not either pressurise c5 or protects d6, force an exchange on c5 and you can win easily