Many correct solutions received to this. Approaches varied, but most took the normal route of logic problems. Here I present a different approach: brute force and ignorance. There are only 120 permutations of five elements, so 120^2 total potential solutions to consider. This only comes in at 14,400 different cases to consider - well within the capabilities of your browser.
For details, look at the page source.
The dyer's name was Farmer.