NL-NWO 2005 Problem 3

Let $a_1,a_2,a_3,a_4,a_5$ be distinct real numbers. Consider all sums of the form $a_i + a_j$ where $i,j \in \{1,2,3,4,5\}$ and $i \neq j$ . Let $m$ be the number of distinct numbers among these sums. What is the smallest possible value of $m$ ?