From my understanding of the question, the following is my answer.
Let width and height of the shelves be w and h respectively.
Given, w = 5h ------------------(1)
and perimeter of the shelves = 2(w+h)
but there are 2 extra wooden brackets so that the set of shelves contains 3 shelves
So the total wood = perimeter of the set of shelves + width 2 extra wooden brackets
So, 80 = 2(w+h) +2w
or 80 =4w +2h
or 80 = 4(5h) +2h
or 80 = 22h
or h = 80/22 = 40/11
Putting the value of h in eq(1) we get:
w = 200/11
So the width of the set of shelves should be 200/11 feet and its height should be 40/11 feet