It really comes down to how to capture the h-pawn- with the rook or the king. If black captures with the rook, white will find a draw in this position:

1.....Rxh3 2.Ke5 Kg4 3.Rg2+ Rg3 4.Rxg3+ Kxg3 5.Kxf5 h5 6.Kg5 h4 7.f5=

It won't help black to play 3....Kf3 either since white can just reply with 4.Rg5 leading to another drawn rook ending.

However, if black captures with rook, black can preserve the f-pawn while winning both white pawns, or getting a too face h-pawn. The most critical line I can see this one:

1.....Kxh3 2.Ke5 Kg4 3.Ra7 Re3+ 4.Kf6 h5 5.Ra5 h4 6.Rxf5 h3

And now white can't both protect the f-pawn and stop the h-pawn.....

7.Rg5+ Kxf4 8.Rh5 Kg3-+

The other critical line where white just concedes the f-pawn in order to win the h-pawn just leads a lost ending:

1.....Kxh3 2.Ra7 Kg4! 3.Rxh7 Kxf4-+

It might continue like this....

4.Rh4+ Kg5 5.Rh8 f4 6.Rg8+ Kf5 7.Rf8+ Kg4 8.Ra8 Re3

And the white king will not be able to aid in the defense of the f1 square.