Yeah it has to be f5. The reason it's the right move is that at this stage in the game the goal is to get your king in a position where it can block the opposing king from taking your pawns.
If black takes the pawn on f5, then white can move the king to f5. If black moves to e2 to try to protect that side then white can just switch back to controlling the left side by going to e5.
If black doesn't take the pawn, if they try to move their king to e2 to control the right, white can move the pawn to f3 to check the king and force the king to take it leaving the left side wide open for white. And of course, if black doesn't move their king to the right then white can just take the pawn and have completely control of the right side anyway.
So eventually, barring any kind of blunder, white will be able to promote a pawn, but black will never be able to with this setup as long as white plays f5 here.
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Rook x F7
King H6 (everything else is mate in 2)
Rook x H7
King G5
Bishop E7 mate
Without knowing it's mate in 3 I most likely would have missed Bishop E7 in a game and tried to force some trades and promote a pawn since it's a winning position anyhow.
I play 2… d6 then usually take on f4 next move to transpose into Fischer defense. I think this move order is better because it tempts some 3. Bc4 players to play Nf3 attacking your pawn, when you can transpose. If you don’t want to learn theory then just play the KGD with 2… Bc4 and 3… d6. In both lines white can’t play 3. fxe5 due to 3… Qh4+.
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