Mate in 5 Exercise 25

White plays and wins in 3 moves https://lichess.org/ZTR13ESp

1. Kh6 Ne7 2. Ra8+ Ng8+ 3. Rxg8#

The analysis board does checkmate in 5 moves

1. Kh6 Nc7 2. Kg6 Ne8 3. Rf7 Nf6 4. Rf8+ Ng8 5. hxg8=Q#

I don't understand why the white tower didn't capture the black horse.

Source:

https://www.amazon.com/Chess-Puzzles-Advanced-Expert-Level/dp/B0917YQZP1