The positive differences $a_i-a_j$ of five different positive integers $a_1, a_2, a_3, a_4, a_5$ are all different (there are altogether $10$ such differences). Find the least possible value of the largest number among the $a_i$.
Problem
Source: 2004 Estonia National Olympiad Final Round grade 9 p2
Tags: min, max, Difference, algebra