If a person did not die in the first five years of their life, they could expect to live to be sixty to seventy years of age before dying. Since child hood mortality rates were so high, the average life expectancy was dragged down. 15-20 is much lower than any source I've seen, but several books about Ancient Mesopotamia or Medieval Europe place the average life expectancy around forty years. Yet with a childhood mortality rate of around fifty percent, that drags the life expectancy down.
Sources: "A Distant Mirror" by Barbara Tuchman
"Cultural Atlas of Mesopotamia and the Ancient Near East" by Michel Roaf

When you say "ancient times", what time period are we talking? Classical Era? Bronze Age?