I don't think a pawn breakthrough works because the white king is in time to stop any pawn that gets through. 1...a5 2.bxa5 b4 3.axb4 d4+ ( surely not 3...cxb4 4.cxb4) 4.cxd4 cxb4 and now whites king is in time to scoop up the b pawn and since he now has the farthest outside passed pawn he wins. If on the other hand 1... a5 2.bxa5 Kc6 was the plan then I guess it's actually more straight forward than the continuation I would have played.
@Peter-Ashley-2 Patience, I think. Mainly patience. The computer seems to suggest d4 followed by c4 and Kd5, which looks good positionally and may work for a good endgame player. In any case, I believe positionally black is better anyway and his best bet is to slowly work towards a break-through. He probably will have one at some point; white never will.