Since we are trying to find the values of two variables (the length L and the width W), we need at least two equations. The perimeter of the rectangle is 42 inches, and the length is 5 inches longer than the width. Mathematically, we get our two equations from these two statements.

First, since the perimeter is 42 inches, we add the four sides and get L + L + W + W = 42. Adding like terms gives us

2L + 2W = 42

Next, the length is 5 inches longer than the width, so

L - 5 = W

We then solve these two equations for L and W. I will use substitution, but elimination would also work.

2L + 2W = 42

L - 5 = W

2L + 2(L-5) = 42

2L + 2L - 10 = 42

4L - 10 = 42

4L = 52

L = 13

Having solved for L, we can now substitute 13 for L in L - 5 = W to solve for W.

13 - 5 = W

W = 8

Our final step is to check by plugging our values into the original equations and making sure they work:

2(13) + 2(8) = 42 (Correct)

13 - 5 = 8 (Correct)