could I win?

g4 is a mistake, I belive, because it gives white a protected passed pawn...
and for h5 the king should come not the rook and there is no way to save the pawn for too long...

The final position looks hard to win. Maybe already a draw. (I can't see how black can win if white plays h4 immediately, for instance).
However, at least at one point during the endgame, I think you had a way to reach a winning position:
Instead of 59...Kf5, you should have exploited the fact that Rc6 temporarily can't harrass your king if your rook leaves and go for 59...Ra5 (threatening to infiltrate on a1 or a2. Now, winning the g5 pawn will be lost for white if he allows the rook to infiltrate on a2-d2 in return) 60.Rc8 (This should have been black's previous move probably) 60...Ra1 and I don't think black can hold:
61.Re8+ Kf6 62.Re2 (Kxd4 c2 just loses immediately) Rg1 63.Kxd4 Rxg3, and now, white can't hold on to the h3 pawn: 64.Rh2 Kg6 followed by Kh5-h4. It's over.
When you're given a chance to infiltrate with your rook, examine it closely, even if it seems to drop material in the short run.

grolich - thanks... noted... I think you confused beetwin black and white few times but I understended...
superpotato - thanks , I really couldn't think of it
grolich - thanks... noted... I think you confused beetwin black and white few times but I understended...
superpotato - thanks , I really couldn't think of it
Going over it, no i didn't get confused between black and white, so if something is not clear in what I've said, please ask.
(Now that I look at it, you may simply refer to me saying that winning the g5 pawn is lost for white... which is true. Only white can "win" that pawn (heh it's black, after all), but the position would be lost for him if he does:)
If there are any further misunderstanding, please let me know.

61.Re8+ Kf6 62.Re2 (Kxd4 c2 just loses immediately) Rg1 63.Kxd4 Rxg3, and now, white can't hold on to the h3 pawn: 64.Rh2 Kg6 followed by Kh5-h4. It's over."
" 60.Rc8 (This should have been black's previous move probably)"
the bolded lines are confusing me...
by the way: from where in Israel are you?

I suppose I don't have to remind you, Ramat Aviv is part of Tel Aviv.
I live in Tagor...
Funnily enough, I don't get to play there much, but I play at another club.
I have to agree with EnglishChessPlay. Other than a few minor misses (most of which I would have made myself during a real game... maybe all of them), this was a very good game.
I've played the following game 8 hours ago, any comments that might help me?
because of the ratings I'm quiet happy about this game...