[FEN "8/4k2p/p1b1p1pP/Pp1p2K1/1PpP1P2/2P1R3/8/8 b - - 0 1"]

Houdini6.02 eval flatlines at 1.37, but I reached d= 54 , and , although the eval continued to flatline, the main line indicated White pushed the f4 pawn in f5 toward the end. I started a trial with the pawn already in f5 , Black to move, and White won. Still I am not sure because Houdini 6.02 could have missed a possible defense against the f5 push. Can Black defend against the f5 push without deteriorating the position ( maybe allowing the White rook to penetrate its position)? Or the position is a win for White , albeit slowly? Just for curiosity , if the verdict is draw , can White win in absence of the 50 move rule?