Difference of pawns structure in pawns endagames

Hello everyone, I'm analyzing a game I just played and I cannot understand why after 37. d5 by black the endgame is winning for white. Why is the pawn so much better in d4? Is it because on d5 is closer to f5 and at some point white king will be able to attack both?

[Event "Rated Classical game"]
[Site "lichess.org/DJkTvTyC"]
[Date "2021.01.30"]
[White "andreatetta"]
[Black "orjin"]
[Result "1-0"]
[UTCDate "2021.01.30"]
[UTCTime "10:36:30"]
[WhiteElo "2014"]
[BlackElo "1983"]
[WhiteRatingDiff "+27"]
[BlackRatingDiff "-6"]
[Variant "Standard"]
[TimeControl "900+15"]
[ECO "B93"]
[Opening "Sicilian Defense: Najdorf Variation, Amsterdam Variation"]
[Termination "Normal"]

1. e4 c5 2. Nf3 d6 3. d4 cxd4 4. Nxd4 Nf6 5. Nc3 a6 6. f4 e5 7. Nf3 exf4 8. Bxf4 Be7 9. Bc4 Nh5 10. Bxf7+ Kxf7 11. Qd5+ Be6 12. Qxh5+ g6 13. Qh6 Bf8 14. Qg5 Qb6 15. Nd5 Qa5+ 16. c3 Bxd5 17. exd5 Be7 18. Qg4 Qxd5 19. O-O h5 20. Ng5+ Kg7 21. Ne6+ Kh7 22. Qe2 Nc6 23. Nc7 Qc5+ 24. Be3 Qe5 25. Nxa8 Rxa8 26. Rae1 Re8 27. Bd2 Qc5+ 28. Kh1 Ne5 29. Bf4 Bh4 30. Bxe5 Rxe5 31. Qd2 Rxe1 32. Rxe1 Bxe1 33. Qxe1 Qe5 34. Qf2 Qf5 35. Qxf5 gxf5 36. Kg1 Kg6 37. Kf2 d5 38. Kf3 Kg5 39. g3 Kg6 40. Kf4 Kf6 41. b3 b6 42. a4 a5 43. h4 1-0

The pawn is vulnerable at d5 and also at d5 it no longer controls central square e5. After 37...d5 the white king can invade.

Pawn endgame = brute force calculation