This problem demonstrates Galileo's law of odd numbers . For a body falling freely from rest, the distances traversed during equal intervals of time stand to one another in the same ratio as the odd numbers beginning with unity (1: 3: 5: 7...).

1. Identify Conditions: The stone falls under gravity (uniform acceleration, $a=g$) starting from rest ($u=0$). The time intervals are equal ($t = 5$ s).
2. Apply Galileo's Law: Distance covered in the 1st interval ($h_1$) is proportional to 1. Distance covered in the 2nd interval ($h_2$) is proportional to 3. Distance covered in the 3rd interval ($h_3$) is proportional to 5. Therefore, the ratio is $h_1 : h_2 : h_3 = 1 : 3 : 5$.
3. Formulate Relation: From the ratio, we can write: $\frac{h_1}{1} = \frac{h_2}{3} = \frac{h_3}{5}$ $h_1 = \frac{h_2}{3} = \frac{h_3}{5}$