My first thought was that two balls identical apart from mass would take the same time to fall.
Thinking about it a bit more I would put my money on the heavy ball falling faster.
Here is how I would explain it;
Newtons Second Law gives F=ma
where
F is the force on the body
m is the mass of the body
a is the acceleration of the body in the direction of the force
If we take the two balls and drop them, at the same time, from the same height, in a vacuum they will both hit the ground at the same time.
The masses of the balls were different, but their acceleration was the same (they hit the ground together), so the gravitational force on the balls must have been different.
Now lets play a mind game and suppose that gravity would exert the same force on each ball, if we ran our experiment again what would happen?
In this case because F=ma (but we have said the force on both balls is the same) the ball with the smaller mass must accelerate faster and so would hit the ground first. In other words the same force accelerates the smaller mass more.
Now lets consider dropping the balls in air (with normal gravity).
The dimensions of the balls are identical so the air resistance on both balls, even though they have different masses, will be the same and will just depend on the speed of the ball.
However if both balls accelerate at the same rate they will be traveling at the same speed but that means both balls will experience the same resistive force and the resistive force will affect the smaller mass more. As a result the lighter ball will hit the ground last.
I would go for photosensors to detect the the start and end.
On earth the acceleration due to gravity is approximately 10m/s/s.
As a result a drop of 5m would take 1s.
Six stories seems a bit high.
What would be great though would be a sealed 5m perspex tube attached to a vacuum pump.
You could do the experiment with and without air.
An electromagnet could be used to drop the balls inside the tube.