let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

The length of a rectangle it 11 centimeters less than five times its width:

l = 5w - 11

Its area is 36 square centimeters

l*w = 36

plug l = 5w - 11 into the last equation:

(5w - 11)*w = 36

by solving we find:

w = 4 cm

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

l = 5*4 - 11

l = 9 cm

the dimensions of the rectangle are 4 cm and 9 cm.