Because they are one of the best ways of measuring the wellbeing of children. An improvement in mortality rates for a health district from one year to the next is a good way of showing that the wellbeing of children in that district is improving. An increase in the mortality rates indicates that the wellbeing is deteriorating. A high mortality rate draws attention to that district where there is obviously a problem.
The under-5 mortality rate is one of the best methods of assessing the wellbeing of children.
The 4th Millennium Developmental Goal set by the United Nations is to reduce the under-5 mortality rate between 2000 and 2015 by a third.