what about this?
- I think this doesn't belong here, this is an approach to a "standard" shimari since black plays 3 it is not a 4-5 joseki anymore.
it went like this in my game. there were only hoshi stones at the rest of the board. was it a mistake to invade or did he make a mistake in the joseki?
AJP: Definite mistake to invade. Way too early for this. I would just play at , seal white into the corner or press white low on the upper side, end in sente and use the black wall for a moyo. Black's high shimari means black is looking for influence (otherwise black would have made the low shimari) and white invading like that just gives black what he wants. may have use as a probe later, when it is less clear whether the corner is more or less valuable than the outside, but certainly not when there are only hoshi stones on the rest of the board.
MrTenuki: in the second diagram doesn't look right, because black can now kill the white group:
(I moved your one line higher because this leaves less aji.)
The placement denies an eye in the corner. seeks to make ko, but destroys the second eye. Now Black has miai to kill the white group: if white plays cuts off by playing at a, black kills by playing at c; if white plays at b, black connects back home with a. And thanks to the fact that the White suffers from a shortage of liberties, a clamp at d isn't even possible.