Chesscademy Tactic: Is my alternative as good as the right answer? I've been playing with the Chesscademy app for a while, solving some tactics (which I'm not sure is improving my chess, but it's a good puzzle to kill some time). Today I ran into one tactic that I failed to solve, though my play seemed to result in the same advantage as the one picked as an answer.

Since I'm a beginner at Chess, I might be missing something about the move that makes it a better candidate, so I decided to post it here and get some opinions.

Below is the move that the tactic claimed is right (Black then White):

[FEN "r1r4k/1p5R/3b4/4q3/B3P1Q1/1n1P3P/6P1/5R1K b - - 0 1"]

1... Kh7 2. Rf7 Kh6 3. Qh4 Qh5 4. Rh7 Kh7 5. Qh5+


My answer was basically the same, except instead of 3. Qh5 Rh7 I played 3. Qh5 Rf6.

So I could foresee one outcome from that play:

[FEN "r1r4k/1p5R/3b4/4q3/B3P1Q1/1n1P3P/6P1/5R1K b - - 0 1"]

1... Kh7 2. Rf7 Kh6 3. Qh4 Qh5 4. Rf6 Kg7 5. Qh5 (Kf6 6. Qh6) 


That opens up an X-ray attack on the bishop if the King captures the rook (5. Kf6 Qh6), though it can be easily defended if the king goes to a square next to the bishop.

Is there any reason why this play is worse than the original answer? Usually, when I thought I was right about a play I'd think for a while and find some reason why it was not a good one, but this time I'm not really figuring out why the original answer would be better than this one.
The problem is that 5. Qxh5 isn't check, so Black has time for some back rank tricks (instead of capturing the rook on f6):

[FEN "r1r4k/1p5R/3b4/4q3/B3P1Q1/1n1P3P/6P1/5R1K b - - 0 1"]

1... Kxh7 2. Rf7+ Kh6 3. Qh4+ Qh5 4. Rf6+ (4. Rh7+ Kxh7 5. Qxh5+) Kg7 5. Qxh5 Rc1+ 6. Qd1 Rxd1+ 7. Rf1 Rxf1#