Plug in x = 1 to get...
f(x) = 5(2)^x
f(1) = 5(2)^1
f(1) = 10
So the point (1,10) is on this curve
Do the same for x = 5
f(x) = 5(2)^x
f(5) = 5(2)^5
f(5) = 160
The point (5,160) is also on the curve
Use the slope formula now
m = (y2-y1)/(x2-x1)
m = (160-10)/(5-1)
m = 150/4
m = 37.5
The average rate of change is 37.5