I assume you understand how we got to 15 points in total, that's easy enough. I don't know why you want to use sets for this though. It's more of a simple logic problem.

You know the maximum number of points one team can score is 6.

You also know 5 + 4 + 3 + 2 +1 = 15

If team 1 scores 5 + 1 = 6 (the maximum, because we want to assign as many points as possible to the first two teams)

Then team 2 can also score 4 + 2 = 6 (another maximum)

6 + 6 = 12

So we only have 3 points left, since the other teams scored the maximum number of points.

This is the minimum number of points left, and it goes to team 3.