Question about knight vs. 3 pawns endgame In the following puzzle, 5. Kb6 is considered better than 5. Kc7. Doesn't Kc7 force Black to sacrifice his knight (sooner)?

[FEN "8/3n4/8/1P3k2/1P6/4K2P/8/8 b - - 0 1"]

1... Nb6 2. Kd4 Ke6 3. Kc5 Nd7+ 4. Kc6 Ne5+ 5. Kb6 Nd3 6. Ka5 Kd7 7. h4 Nf4 8. 
Ka6 Nd5 9. h5 Nxb4+ 10. Ka5 Nd5 11. h6 Nf6 12. Ka6 Kc7 13. Ka7
After 5. Kc7 it is a draw, e.g

[FEN "8/3n4/8/1P3k2/1P6/4K2P/8/8 b - - 0 1"]

1... Nb6 2. Kd4 Ke6 3. Kc5 Nd7+ 4. Kc6 Ne5+ 5. Kc7 Nd3 6. b6 Nb4