Joonas Tyystjärvi: Supposing that the cutting point to the right of is not usable, does this work? It seems to me that after , White is alive - are Black's moves correct? (Of course, the result is locally very bad for White.)
'a', 'b', and 'c' (followed by 'd' if white connects) are all more important than taking one stone. When seeking to kill, it is important not to try and separate your opponent's stones. It is better to squish them all together into an area too small to live.
White 5, incidentally, is not that strong. It gives up on the option to descend straight down, or play one to the left. Defending 1 with a hanging connection (for the ko) really is the best white can attempt for move 5. In fact, playing this sooner rather than later may be better -- 3 for 4 might be possible as a ko threat during the fight.
I think Black can kill by playing at instead. If Black omits , then White a Black b makes life - Andreas