I am fascinated by this social experiment. Correct me if I am wrong, though, @manniman, but I think @geekgirl said that she was removing the initial "5" identifying the first piece. This means there is no way of knowing which piece goes first, and so there are 120 possibilities, rather than only 24, actually. (5x4x3x2x1=120)
If each person tries an equal number of them, that is 30 combinations per person to try.