Call x and y those angles. If they are complementary, then their sum equals 90°:
x + y = 90°
y = 90° - x
The ratio of them is 5 to 1. So,
x/y = 5/1
x/(90° - x) = 5/1
x = 5 * (90° - x)
x = 450° - 5x
x + 5x = 450°
6x = 450°
x = 450°/6
x = 75°
The measure of the other angle is
y = 90° - 75°
y = 15°
The angles are 75° and 15°.
I hope it helps. =)
