First, we need to calculate the new charges for both balls. Since one ball has five times the charge of the other, let's call the smaller ball's charge x. This means the larger ball's charge is 5x. When the balls touch, they will share their charge evenly, so the smaller ball will now have a charge of 3x and the larger ball will have a charge of 3x as well.

Next, we need to calculate the new force of interaction between the two balls. This is done by using Coulomb's Law, which states that the force of interaction between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Since the charges are now 3x and 3x, their product is 9x. The distance between them is the same as before, so that remains constant. Therefore, the force of interaction between the two balls has increased 9 times from its original value.

In simpler terms, the bigger charge on one ball combined with the smaller charge on the other ball creates a much stronger force of attraction between the two when they are brought into contact.

So to sum up, the force of interaction between the two charged balls has increased 9 times due to the difference in their charges, resulting in a stronger pull between them.