First, we draw a picture. Setting the line and parabola equal to each other, we see that the points of intersection are at
and so x=1 or x=4. This gives the following picture.
The white area is what we want to rotate. Let x be a point between 1 and 4. Then the radius of a shell is r = 5-x. The height of a shell is . Thus, when we rotate about x=5, the height will move a distance of and hence, the volume of revolution is