5. There are 19 children with ages ranging from $1 \sim 19$ years old standing in a circle. Record the difference in ages between each pair of adjacent children. The maximum possible sum of these 19 differences is . $\qquad$
5. 180 .
19 differences are derived from 19 equations, where each integer from $1 \sim 19$ appears twice. To maximize the sum of the differences, the larger numbers 11 and 19 should all be used as minuends, and the smaller numbers $1 \sim 9$ should all be used as subtrahends. The number 10 should be used once as a subtrahend and once as a minuend. Therefore, the maximum value is
$$
2 \sum_{i=11}^{19} i-2 \sum_{i=1}^{9} i+10-10=180 .
$$

In fact, the larger and smaller numbers can be alternately arranged in a circle, and the number 10 can be inserted at any position.