#### Answer

The smaller angle is $15^{\circ}$ and the larger angle is $75^{\circ}$.

#### Work Step by Step

The ratio given is 1:5, and it is stated that the angles are complementary, therefore
$1x+5x=90$
Simplify...
$6x=90$
Divide both sides by six...
$x=15$
If $x=15$, then the smaller angle ix $1x=1(15)$ or $15^{\circ}$ and the larger angle is $5x=5(15)$ or $75^{\circ}$.