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!

i cant see a problem with it, but when the computer plays, it always wants to do the mate in 5, but when i verse the CPU, i get it in 4. weird.

Hi Cazaron,

So, you are confirming that my solution of the mate in 4 is correct?  

I must be missing something obvious, because...

move Rg1, the same rook that just moved, then kh4, Rh6# mate

1. Rh1, leading to:

1. ...  Kh5 2. Rg1 Kh4 3. Rh6#

1. ... Kg4 2. Rg6+ Kh5 3. Rg8 Kh6 4. Rh1#

1. ... Kh4 2. Rg6 Kh5 transposing to the previous variation.

Thus mate in 4.

Perhaps they use the mate in 5 to illustrate the theme rather than finding the quickest mate.

Hi Searching4Bobby,

Sorry to confuse, hence, ConfusedConfucius; I meant to write, 3. Rfg1 instead of Rag1.

Phmilet, maybe you're right now that I think about it.  A previous lesson was on having the rooks work like a "ladder" to force the King to a mate.  But, it would have been nice if they had made a notation on this and indicate that although this example lesson could be mated in 4, 5 was chosen to illustrate the "ladder" effect of Rooks. 

whats this?

some chessmaster tutorial thing.