Your neat ratio of 5 blue-eyed to 15 brown-eyed (if indeed only two colours are implied) makes me think of the Mendelian inheritance of eye-colour: but a logical and observant tribe should already have deduced that fact for themselves, without having to hear of the visitor's family and see the visitor's eye-colour.
Thus, a mother who bore a brown-eyed child to a blue-eyed father would realize she must have brown eyes, and kill herself. The father would realize from his partner's suicide that he must have blue eyes, and kill himself. And the child, grown to adulthood, would realize from tales of her parents' suicides that she must have brown eyes, and so kill herself.
Tut. Tragic. But presumably not the answer.

Grant Hutchison