Is puzzle https://lichess.org/training/qsUWV cooked?

For puzzle lichess.org/training/qsUWV, I tried Kd5, which was reported as 'wrong'.
The 'correct' move is f5.

I couldn't tell why, so to learn something, I turned on Stockfish, which from the start showed both firs moves winning, albeit f5 'by more'. But as the analysis deepened, both started coming back with very close winning advantages around +8 or +9.

Did the system make a mistake? Or is there something extra-deep that shows f5 is the only win or much more decisive?

@jonfrankle

First play the move f5, then after rook rf8, then comes Kd5.
I tried the puzzle...

At depth 41, Stockfish (3 lines output) gives a draw for Kd5, and 8.9 for f5 so puzzle seems OK.