Mrs. Johnson is baking cookies for a school event. She needs to make 3 different types of cookies: chocolate chip, oatmeal raisin, and sugar cookies. She wants to use 1/3 of the total flour for chocolate chip cookies, 2/5 of the remaining flour for oatmeal raisin cookies, and the rest for sugar cookies. If she has 15 cups of flour in total, how many cups of flour does she use for each type of cookie, and how much flour is left for the sugar cookies? Let's think step by step and output the final answer within \boxed{}.
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