The average age of a family of 5 members is 20 years. If the age of the youngest member of the family is 5 years, then what was average age of the family at the time of birth of the youngest member?

The family averaged 18.75 years when the youngest was born.

Present total age = 5 x 20 = 100 years.

The youngest is 5, so the other 4 members total 100 - 5 = 95 years now.

Five years back those 4 were each 5 less : 95 - 4 x 5 = 75 years.

Their average then = 75 / 4 = 18.75 years.