Puzzle 41226: Equally good solution not accepted

en.lichess.org/training/41226

The suggested solution starting with Qe8 is a mate in 5.
The solution I came up with also results in a mate in 5
as far as I can tell, yet it is not accepted:

1. Qg8+ Kh6 2. Rd7 Bg3+ 3. Kxg3 Qf2+ 4. Kxf2
if 4... Nf8, 4... Ng5 or 4... Ng7
then 5. Qg7#
else 5. Rxh7#

Also: 1. Qg8+ Ng7 leads to an even quicker mate.

Am I missing something?

Qg8 certainly works, the best way to deal with these puzzles is to downvote them until they are no longer given out.