The question is basically asking you to make a straight line between those two points and find its gradient.
The first step youd best take is to find the coordinates of the points needed so:
f(1)=1^3-1 . f(5)=5^3-5
=0 =120
therefore coordinates are:
(1,0) and (5,120)
the general form of a gradient is:
m=(y2-y1)/(x2-x1)
so plug in your values and you get
m=(120-0)/(5-1)
=120/4
= 30
so your average rate of change between those two values is 30
Hopefully this has been clear enough, good luck
