$\begin{array}{l}V(r)=\frac{4}{3} \pi r^{3} \\ V(r+1)-V(r-1)\end{array}$

Step 1 ：The problem is asking for the difference in volume of two spheres, one with radius r+1 and the other with radius r-1. The volume of a sphere is given by the formula \(\frac{4}{3} \pi r^{3}\). To find the difference in volume, we need to subtract the volume of the sphere with radius r-1 from the volume of the sphere with radius r+1.

Step 2 ：Substitute r=5 into the formula, the difference in volume between a sphere with radius r+1 and a sphere with radius r-1 is approximately 636.70 cubic units.

Step 3 ：Final Answer: The difference in volume between a sphere with radius r+1 and a sphere with radius r-1 is \(\boxed{636.70}\) cubic units when r=5.