let

l = the length of the table, l>0

w = the width of the table, w>0

A = 48 ft^2 is the area of the table

the lenght of a rectangular table top is 8 feet shorter than 5 times the width:

l = 5w - 8

the area of the table top is 48 square feet:

A = l*w

l*w = 48

plug l = 5w - 8 into the last equation:

(5w - 8)*w = 48

by solving we find:

w = 4 ft

click here to see the step by step solution of the equation:

l = 5*4 - 8

l = 12 ft

the dimensions of the table are: the length is 12 ft and the width is 4 ft.