Looks pretty bad to me, doesn't it just hang g3?
By the way, I can't see what's written in the comments boxes on the right hand side of your screenshot. You might want to try making it smaller.
Bad move? Not really.
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Fair point Nachtwulf. But as you said, it removes all the stress on Black's position. Exchanging a pair of pawns doesn't make any progress for White. I think the right(?) idea might have something to do with Black's rook, which is completely inextriacbly trapped by White's bishop (note it blockades b7 too). So I think a rook move. Rc2 or Rf8 would probably be something I'd play. Then see if there's a way to get your king to f5 then e6.
I accidentally edited my previous post to be my new one. Oh well, I forgot what I said before.
***SPOILER ALERT***
Okay, not knowing the answer was killing me, so I went to do the problem myself. Apparently, the answer is pushing the b-pawn and forcing the pawn trade, so white gets a bit more queenside space. Later on, white wins by quickly alternating kingside and queenside threats, winning the h-pawn (the bishop does end up at e3, and the rook goes first to h8 to threaten the pawn and draw in the king as a defender, and Rh6+ decisively wins black's wingpawn).
Heh, looks like it's far more prosaic than my random ideas then 
Out of interest, did you force the trade on b5 or on a6? Because I don't like the idea of releasing that rook before it's necessary!
First, the Bxg3?? pawngrab hangs the B to Rg8+.
@NachtWulf "Apparently, the answer is pushing the b-pawn and forcing the pawn trade, so white gets a bit more queenside space."
Really? I think b5 is beside the point -- black's rook is so bad -- b5 seems like a detail, not the main idea. After the pawn exchange, the issues on the board are: The h pawn is weak, the black rook has no moves and if the White King could get to f5-e6 it would be game over. Isn't there some way to put this together.
My idea is Rg8+ -- with the idea of an eventual Rg5 winning the h pawn or a possible exchange sac if the conditions are right for the king to penetrate. h4 is also a resource to keep handy because Bxg3 is >not< available when the king is on the g-file (because of the rook skewer the mentor author apparently missed).
I just did the analysis on a chess.com diagram and it sure seemed like it worked...but I lost all the work to the wretched jabbering nihilistic God of Internet Timeout and I don't have time to redo the work.
Don't worry, I got the problem wrong several times before guessing correctly! This was the move order (Note: OP's picture starts at move 5):
5.b5 axb5
6. axb5 Kf6
7. Be3 e6
8. Rh8 exd5
9. Kxd5 Kg6
10. Rh6+, winning the pawn.
@JG27Pyth: I believe you're right that the a and b-pawn don't have much influence. I think the explanation for the nit-picky move was probably the fact that this was taken from an actual game, where that move might have been a safety precaution, or perhaps something that bought a little time. (Going purely by conjecture, when one GM annotates/makes a puzzle out of another GM's game, he or she probably wants to have an explanation ready for every move, trivial or not--at the cost of public image.) Anyway, when one has a definitive advantage, it doesn't hurt to further simplify the situation to guarantee the win.
OK, I made the pic smaller. Now can you read it?
-waller- wrote:
Looks pretty bad to me, doesn't it just hang g3?
By the way, I can't see what's written in the comments boxes on the right hand side of your screenshot. You might want to try making it smaller.
Nope, not without losing the bishop for Black, as described. My comment was a quip.
Yep, now we can read it, and now I see your quip!
Nachtwulf, thanks for the line. I think the analysis that the b5 push is merely a safety move and beside the point of the problem is probably accurate, and that the real thing one should see here is the Be3 Rh8 Rh6+ idea. I guess the blocking of the rook does come into play - Black plays Kf6 to move e6 and free his rook - but this allows Rh8 by blocking the bishop.
I love problems like this. There's always more to see, the more you look at it.
-waller- wrote:
Yep, now we can read it, and now I see your quip!
Nachtwulf, thanks for the line. I think the analysis that the b5 push is merely a safety move and beside the point of the problem is probably accurate, and that the real thing one should see here is the Be3 Rh8 Rh6+ idea. I guess the blocking of the rook does come into play - Black plays Kf6 to move e6 and free his rook - but this allows Rh8 by blocking the bishop.
I love problems like this. There's always more to see, the more you look at it.
The Be3 Rh8 Rh6+ line is right. One could well have started this without the b5 line with nearly the same result (two passed pawns).
Oh hey actually, I think we might be missing something about those b pawns. By pushing b5, black is in zugzwang. If black captures, white recaptures, and black is back in zugzwang. Black's rook is obviously stuck, and if the bishop moves, the pawns can be pushed. Even though white has the threat of Rg8+, black can cause complications by pushing the h-pawn if white pushes.
Thus, the king has to move away from the h-pawn, allowing white to attack it with the rook with tempo, then earn the pawn with check (since white still would have the initiative).
I'm gonna do that and see what happens...
--from The Open File, Chess Mentor
OK, pic made smaller. This is a JPEG image. The image I downloaded beloe is a PNG image with better image resolution. The scripted correct move here was b5.