What is the cheapest unique in Path of Exile?
Not really. I don't think there is any unique that's as cheap as 5 chances. Cheapest uniques are the ones that aren't very useful and with low rolls, and even those can be sold for at least 2 alchs (1 alch = 4 chances).
That's based on Hardcore League economy at least, i don't play default league so i don't know are their rates any different.