we will assume the table is rectangular

let

l = the length of the table top

w = the width of the table top

the area of a table top is 57 square feet:

l*w = 57

twice the length is 5 feet shorter than four times the width:

2l = 4w - 5

l = (1/2)(4w - 5)

we need to find the perimete: P = 2(l + w)

plug l = (1/2)(4w - 5) into l*w = 57:

(1/2)(4w - 5)w = 57

by solving we find:

w = 6 ft

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

l = (1/2)(4*6 - 5)

l = 9.5 ft

the perimeter is:

P = 2(9.5 + 6)

P = 31 ft

the perimeter of the table top is 31 feet.