The odds are against it but certainly! White will lose the pawn @ f4 and will need to keep it's king close as pawn @ b7 progresses. Promotion is a must. White's castle must keep the rest busy.

White wins by first misplacing the Black king: 1.Rg6+! and now: 
 
1...Kxf4 and the king steps onto the white pawn's queening square. 2.Rb6! Rxb6 3.Kxb6 h2 4.b8=Q+ and 5.Qxh2 is a simple win. 
 
1...Kf3 also has a major drawback: 2.Rb6 Rxb6 3.Kxb6 h2 4.b8=Q h1=Q 5.Qa8+! (or 5.Qb7+) picks up the dark lady thanks to a skewer. 
 
1...Kh4 also loses the black queen to a nice skewer: 2.Rb6 Rxb6 3.Kxb6 h2 4.b8=Q h1=Q 5.Qh8+ etc. 
 

draw

If i were black i think i could draw or win if white makes a wrong move. As white i think i could play for a draw by +Q then ...RxQ 2.KxR from there i see that Black can make enough of a threat to promote his pawns that white's K is too far away to win the last pawn and the only way to prevent the last pawn from promoting is to keep the K in perpetual check in a way that will lead to a draw by repetition. If i am missing something i sure want to be told what it is.

chess

Rb6! and white wins

chess

1. Лg5+ Крf3  
(1. ... Крf4 2. Лb6 и пешка на b8 превращается с шахом) 
2. b8Ф Л:b8 3. Кр:b8 h2 4. Лh6 Крg2 5. Крc7 успевает к черной пешке...