Volume of balloon (v)= 500cm³
If it is completely immersed in water, it will displace the same volume water.
So buoyant force would act on it in the upward direction.The child need to apply same amount of force as buoyant force to put it inside.
density of water = 1 g/cm³
So the child needs to apply 5N force to put it completely inside water.
(Note: The density of air is negligible compared t density of water. So you should ignore the mass of air.)