After Kf5 white replies with Nc4 and the only way to avoid losing the a pawn is to play the knight back to the poor square b7 and it is very difficult to see how black can make progress. If the knights are ever exchanged then the position becomes a trivially drawn opposite coloured bishop endgame.
[fen "8/5p2/4pkpp/p1n5/Pp6/1Bb1PP2/2PNK2P/8 b - - 0 1"]
1...Kf5 2. Nc4 Nb7
On the other hand, if black exchanges off the bishop for the knight by Bxd2 then black is left with a good knight versus a bad bishop with a potential distant passed pawn on the king side. (Note that if the white bishop moves then that immediately loses the a pawn.) Black will play moves like g5, Ke5, f5, g4.
Endgames are all about calculation and so black should also calculate carefully what happens if the other minor piece is also exchanged by Nxb3. This opens up the route for white to play a sequence of moves like Kd3-c4-b5, Kxa5 and queen the a pawn. Can white win via this route? The answer is not quite. With correct play black queens the h pawn one move before white can queen the a pawn and as they are on the same diagonal black's queen covers a8.
[fen "8/5p2/4pkpp/p1n5/Pp6/1Bb1PP2/2PNK2P/8 b - - 0 1"]
1...Bxd2 2. Kxd2 Nxb3 3. cxb3 Ke5 4. Kd3 f5 5. Kc4 g5 6. Kb5 g4 7. fxg4 fxg4 8. Kxa5 h5 9. Kxb4 h4 10. a5 g3 11. hxg3 h3! (11...hxg3? {only draws}) 12. a6 h2 13. a7 h1=Q
Is there a useful principle to learn from this?
Calculation is key in endgames. If you watch the top players they don't rush in and play the obvious move when they think they have a winning endgame. They take the time to calculate the position through to the win and only then play the move.