With Black's pawn only one square from becoming a queen, White clearly has little time to reorganise his forces. He needs a quick mating threat and the obvious one is to get a bishop or pawn to d5.
But 1.d4 (threatening d5 mate) is met by h1=Q, and 1.e4 (threatening Bd5 mate) Nxe4 2.d4 lets Black defend with Nc3!
That should suggest the idea of 1.c4 (threatening cxb5 mate) when 1...h1=Q allows 2.d4, when nothing can stop mate in two with 3.d5+, while 1...bxc3 e.p. allows 2.e4! Nxe4 3.d4! and Black's knight can no longer move to c3.
Unfortunately, Black meets 1.c4 with bxc4, when 2.axb4 (threatening b5 mate) is effectively dealt with by b1=Q.
Ah, but if we could lure the pawn from b5 to prevent bxc4, it would all fit together. And that's how to do it.
White plays 1.a4! (threatening axb5 mate) 1...bxa4 2.c4
bxc3 e.p. (or 2...h1=Q 3.d4! and 4.d5+) 3.e4! (threatening Bd5 mate) Nxe4 4.d4! and nothing can prevent mate with 5.Bd5 mate.