Black to move......................

1.Kh8 2.Rxh6+ gxh6 3.e6+ Kg8 4.e7+ Rf7 5.Bxf7#.

Correct.....excellent !

I think the black queen is check by the bishop Bc4+, that mean black have to move first in this puzzle, why is it white have to move first? :)

It doesn't say anything about White to move 1st.

Yup, i didnt relise that.

Erm... Black to move, I look at him in the eye with a quizzical look, wondering why he hasn't resigned when he's a queen down.

.this was just a bit of fun,  obviously black had to resign, but he didn't.........................he just didn't move  [lost on time]  this was not a Chess.com game................but I thought it was an interesting position for an easy puzzle ............................... really wanted him to play on so I could execute the moves list above....................GG

There's nothing to calculate. Black is losing and white has many ways to win, all of them easy and crushing wins.

My way is quickest though?

Don't know and it doesn't matter. No one really cares about the quickest win in a game, and you shouldn't either.

More important is to find the simple win IF others are complicated...Once you have a win, the rest is not important. You shouldn't look for a quicker win in a game once a win is found.

But here EVERYTHING wins simply. Even if the black a and b pawns evaporate all of a sudden, it's still a win on autopilot for black.

I know, but the obvious point of a tactical puzzle is to find a quick mate simply to improve our board visualization skills. And anyway I only looked at the board about 1 second before the forced mate popped out at me. I didn't go in search of it. And if it's an easy forced mate, one shouldn't turn it down surely? It's not at all a complicated mate. 

Time out guys,   I have seen instructional puzzles on this site [chess.com tutorials] that are far simpler than this. Yes this is a 'no brainer'  , but i agree with nuclearturkey, there are obviously unlimited ways of winning this game, but the quickest 'forced mate' in the shortest moves,  IS the best , simplest, and most logical way of finishing this game,    in fact, if white plays the obvious moves, then black will only ever have ONE move in response, IE a FORCED move, and will lose by checkmate, as in the moves given at the top of the page.  So is the quickest mate BEST?    Absoulutely in this example.   I suppose the quickest win isn't always the BEST win : after all, any game can end quickly [fool's mate] and that doesn't give much satisfaction.  That's why I love this game,  great games can be any length providing the outcome is not based on excessive weakness or superior strength................. thanks for your debate guys,  If I post another puzzle, will try and make it more interesting-     Adios Amigos.

Also try and write in a bigger font :p

Font made bigger !