Myra was feeling particularly adventurous at the hair salon one day, and decided to dye her hair. The stylist informed her that she had 10 colors to choose from, 6 of which were shades of black. If Myra randomly selects 7 colors and tells the stylist to choose from those, what is the probability that exactly 5 of the chosen hair dyes are shades of black?
Write your answer as a decimal rounded to four decimal places.