Black to move and win
1.Ne8+ Kh3
2.Qg2 Kh4
3.Nf3+ Kh5
4.Rf5#
I think your solution is right.
But the notation is wrong.
In case of the black to move, it starts with 1...Ne1+.
1...Ne8+ seems to be corrected to 1...Ne1+
The following moves are the answer.
1... Ne1+ 2. Kh3 Qg2+ 3. Kh4 Nf3+ 4. Kh5 Rf5+ 5. Qg5 Rxg5#