Can someone explain how h5 is the best move in this position?
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h5 is best because you are developing your rook and preparing to launch an attack on the kingside, where white is most vulnerable.
White can't stop h4, which is essentially a free move, as on h4 the knight must move because it will be double attacked after pxp. And where the heck is the knight going? After nf4, g5 looks like it traps it. So either white must make room somehow, or play ng5 which looks like a precarious spot. I dunno, white's position is starting to look like a house of cards -- he castled too early, and with the white knight on h3, black looks to have a vicious attack brewing.