When do you get 5 points for a field goal?
A field goal (kicking the ball through the uprights at the end
of the field) is worth 3 points in American football. There is no
"point after" attempt for a field goal.
In contrast, a touchdown (carrying the ball past the goal line)
is worth 6 points and allows an attempt for an additional point
after touchdown, which closely resembles a field goal.