IrMO 2017 Problem 7

$5$ teams play in a soccer competition where each team plays one match against each of the other four teams. A winning team gains $5$ points and a losing team $0$ points. For a $0-0$ draw both teams gain $1$ point, and for other draws ( $1-1,2-2,3-3,$ etc.) both teams gain 2 points. At the end of the competition, we write down the total points for each team, and we find that they form 5 consecutive integers. What is the minimum number of goals scored?