The perimeter is twice the length plus twice the width, or 2x+2y.
Therefore, 2x+2y = 38 as given.
Also, the length is 5 ft longer than the width so x = y + 5
Knowing these equations are true, you can solve.
Substitute for x: 2(y+5) + 2y = 38
Distribute: 2y + 10 + 2y = 38
Simplify: 4y + 10 = 38
Subtract 10: 4y=28
Divide by 4: y=7
x=y+5 = 12
The length is 12, which is 5 more than the width of 7. The perimeter is 2(12+7) = 2(19) = 38
