I have made a decision to improve my endgame, so to use the rare opportunities when I actually play one fully, I submit to you this game (hopefully first of many) for analysis, comments etc. Starting at 52... e5 :

I played this endgame in Live, naturally with time increments, and through what appears to be an opponent blunder won a drawn endgame.

Once he plays ... fg (and then ... e4) it looks lost.  You put your bishop on c6 and then move it to e8, forcing the h-pawn forward so your king can get in (as happened in the game).  Instead, if he plays 5... Kxg5 you are hard-pressed to prevent the exchange of your last pawn.

But I think your 4 h4 was more of a mistake then 5 hg.  It looks like 3 Ke4 was stronger--your winning chances seem pretty bright there.  There are vars like 3... g4 4 hg hg 5 Bd1 Kg5 6 Kxe5 f5 7 Bb3 followed by 8 Bd5.