2001 AMC 12 Problem 4

Let $m$ be the mean. The least number is $m - 10,$ the greatest is $m + 15,$ and the middle number is the median $5.$ Their sum is $3m,$ so $$(m - 10) + 5 + (m + 15) = 3m.$$ This gives $m = 10,$ so the sum of the three numbers is $3m = 30.$ Thus, the correct answer is D.