The given problem is a system of equations in two variables problem. Here we have the width (w) and the length (l) of the rectangle as the two variables.
We're given that the length of the rectangle is 5 feet less than three times its width. This relationship can be translated into the following equation:
l = 3w - 5
We're also given that the perimeter of the rectangle is 30 feet. Since the perimeter of a rectangle is given by the formula 2*l + 2*w, we can write the following equation:
2*l + 2*w = 30
Now, we have a system of two equations which are:
l = 3w - 5
2*l + 2*w = 30
To solve for the variables l and w, we substitute l from the first equation into the second equation. This renders the equation:
2*(3w - 5) + 2w = 30
Simplify this equation by distributing and combining like terms:
6w - 10 + 2w = 30
8w - 10 = 30
Rearranging this equation to isolate w:
8w = 40
After dividing by 8 we get w:
w = 5
Substitute w = 5 into the first equation to find l:
l = 3*5 - 5
l = 10
So, the dimensions of the rectangle are width = 5 feet and length = 10 feet.