Solution
I have to say many of you were very close and actually found the deciding first move: 1. ... Rxd5+!
However the most accurate continuations to win as fast as possible were not found. Let me show you now the fastest ways to win:
1. ... Rxd5+ 2. Kxd5 Rd8+and now
a)
3. Kc6 Qd7+ 4. Kb7 c5+ 5. Kb6 Rb8+ 6. Ka6 Qb7+ 7. Kxa5 Ra8# |
b)
3. Nd6 Rxd6+ 4. Kc5 Qd7! (idea: Qc6#) 5. Re8+ Qxe8 6. Qh1 Qe5+ 7. Kc4 Qd4+ 8. Kb5 Qb4# |
Amazing game, and what a missed opportunity for your unlucky opponent! :)