The expression for the volume of the cuboid is:

V = x^3 + 2x^2 - x - 2

To find the dimensions of the cuboid for x = 5, we simply substitute x = 5 into the expression:

V = 5^3 + 2(5^2) - 5 - 2
V = 125 + 50 - 5 - 2
V = 168

So the volume of the cuboid for x = 5 is 168 cubic units.

To find the dimensions of the cuboid, we need to factor the expression for the volume:

V = x^3 + 2x^2 - x - 2
V = (x - 1)(x + 2)(x^2 + x + 1)

Since the dimensions of a cuboid are typically given as length, width, and height, we can assume that the dimensions are three of the factors of the expression. However, we don't know which factor corresponds to which dimension.

We can use the fact that the volume of a cuboid is given by V = lwh, where l, w, and h are the length, width, and height, respectively. We know that V = 168, so we can try different combinations of the factors to see which ones give us a product of 168.

If we assume that the length is (x - 1), the width is (x + 2), and the height is (x^2 + x + 1), then we can write:

V = (x - 1)(x + 2)(x^2 + x + 1)
V = (5 - 1)(5 + 2)(5^2 + 5 + 1)
V = 4 * 7 * 31
V = 868

This is not equal to the given volume of 168, so we need to try a different combination of factors. If we assume that the length is (x - 1), the width is (x^2 + x + 1), and the height is (x + 2), then we can write:

V = (x - 1)(x^2 + x + 1)(x + 2)
V = (5 - 1)(5^2 + 5 + 1)(5 + 2)
V = 4 * 31 * 7
V = 868

This is equal to the given volume of 168, so the dimensions of the cuboid for x = 5 are:

length = x - 1 = 4
width = x^2 + x + 1 = 31
height = x + 2 = 7

Therefore, the dimensions of the cuboid for x = 5 are 4 x 31 x 7.