Two complementary angles in the ratio 5:7. What is the measure of the smaller angle?

So,

Complementary angles are angles which add together to make 90°.

To find the value of one unit in the ratio 5:7, take these steps:

Add the number of units.

5 + 7 = 12

Divide 90° by 12.

90/12 = 7.5°

The smaller angle is "worth" 5 units.

7.5 * 5 = 37.5°