solution to problem XYZ020 is incomplete

The solution states that black has a draw by perpetual check however and turns out to be true, but white has to play it well otherwise he is checkmated

see diagram below:

White is under no obligation to play 5. h6.  5. Ba4 instead and white is playing for a win or a draw.  If you take the bishop, then the h pawn queens; so it's give the check and take the perpetual.  IMHO (and I'm often wrong) 

EDIT: Oh my bad...You covered the Ba4 line. 

The line with Ba4 is also listed and also leads to checkmate

5.h6?? is a blunder.  6.Ba4 and its a draw, unless white loses his mind and takes the bishop.

No its not see the gray line where white plays Ba4 it leads to checkmate in the same way.

I stand corrected.  Thats what i get for posting to fast, but 5.h6 is still a blunder.

5.Bd1 is what we missed.  Gives the white king an escape square.  I hope...

Maybe 3.h5 is bad and should be Ba4? But that is not what the proposed solution was.

I believe you are correct Sir.

5.Bd1 Bc8+ 6. Kb5 Kb7 7. Ka4

I agree with baddogno. Diagram:

Yes thank you Bd1 is the move that saves white