we will assume that the perimeter of a rectangle is 138 cm.

let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

the length is three less than five times the width:

l = 5w - 3

P = 138 cm the perimeter of the rectangle

P = 2(l + w)

2(l + w) = 138

plug l = 5w - 3 into the last equation:

2(5w - 3 + w) = 138

by solving we find:

w = 12 cm

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l = 5*12 - 3

l = 60 - 3

l = 57 cm

the dimensions of the rectangle are: the length is 57 cm and the width is 12 cm.