Mate in 5 or 4?

Hi all, just purchased the most recent copy of Chessmaster, XI: Grandmaster Edition for the PC.  As I was going through one of their tutorials, Academy-Josh Waitzkin, I came across a lesson where they're indicating a mate in 5.  I say there's actually a mate in 4 and need your confirmation.  Here is the position:

White has a Rook on a1 and b6 and a White King on a8.  Black has his King on g5.  Their solution is 1. White Rb4.. 2. White Ra5..,etc. hence mate in 5.  My solution: 1. Rf1.. 2. Rg6.. 3. Rag1 4. Rh6 mate.  Please confirm.  Thanks!

1.Rf1 Kg4 2.Rg6 Ka5 3.Rfg1 Ka4 4.Rh6 ++ definately works (I assume you meant 3.Rfg1)

Hi rgallagher,

Yeah, made an error on my notation; yes, I meant to write Rfg1.  Thanks for your confirmation.