Let's denote the five consecutive integers as x, x + 1, x + 2, x + 3, and x + 4, where x is the smallest integer among them.

According to the given information, the average of these integers is 15. So, we can write the equation:

(x + x + 1 + x + 2 + x + 3 + x + 4) / 5 = 15

Now, let's simplify this equation:

(5x + 10) / 5 = 15

Now, multiply both sides of the equation by 5 to isolate 5x:

5x + 10 = 15 * 5

5x + 10 = 75

Subtract 10 from both sides:

5x = 75 - 10

5x = 65

Now, divide by 5:

x = 65 / 5

x = 13

So, the smallest integer is 13, and the greatest integer is x + 4 = 13 + 4 = 17.

The difference between the greatest and the least of the 5 integers is:

17 - 13 = 4

Therefore, the difference is 4.