For a set of 5 positive integers, the mean is 4, the mode is 1, and the median is 5. What are the 5 numbers?

Let the 5 integers be a, b, c, d and e (arranged in ascending order).

Since we know that the median is five, we can conclude that the value of c=5.

It's given that the mode is 1. 1<5, and has to be repeated more than once. Therefore, a and b = 1.

Now, the mean is 4. So, (1+1+5+d+e) = 4

d+e=13 (d and e have to be greater than 5)

Which makes d=6 and e=7

In conclusion, the 5 integers are 1,1,5,6,7