Quiz

18 moves. Or 17. Something like that.

Basically, first, rotate the entire caterpillar to the left so that 5 is at the bottom, then don't touch the last column and rotate the remaining 4 (1, 2, 3, 4) to the left. Then move 4 from the top to 5.

Done.

It seems plausible, but could you describe the solution in more detail so I can be sure? Also, please state the exact number of moves.
For brevity, just write the number you're moving at each step, without specifying the direction, because the direction can always only be one (towards the empty cell).
Of course, I'd also like to know why it can't be done faster, but as promised, I won't demand it.