It would make sense to put the larger fish into a larger aquarium.
If you get a divider, you can give the smaller fish two gallons, and the larger one three gallons. You will just have to align the divide either to the left or the right, not in the center. But over time, there will be space issues when the betta is fully grown to two inches or so, and its the same trouble again.
Personally, I would just buy another five gallon. That way, you could include some tank mates as well. I'm not one to put a betta in a tank alone. I always include a few shrimp or frogs.
EDIT: On the age discussion, I'm 13 turning 14 on July 23rd. Just my $0.02. :P