Since the system consists of two bodies attracting each other under mutual gravitational force, there is no external force acting on the system ($F_{ext} = 0$). Therefore, the position of the centre of mass remains stationary.

The initial distance between the centres is $12R$. Collision occurs when the bodies touch, meaning the distance between their centres becomes the sum of their radii: $R + 2R = 3R$. The total distance covered by both bodies is $d_{total} = \text{Initial Separation} - \text{Final Separation} = 12R - 3R = 9R$.

Since the centre of mass is stationary, the distance moved by each body is inversely proportional to its mass ($m_1 d_1 = m_2 d_2$). Let $d_1$ be the distance moved by the smaller mass $M$ and $d_2$ be the distance moved by the larger mass $5M$. $d_1 = \frac{m_2}{m_1 + m_2} \times d_{total}$ Substituting the values: $d_1 = \frac{5M}{M + 5M} \times 9R = \frac{5}{6} \times 9R = 7.5 R$.