Two isolated point masses 2M and 5M are initially at rest in free...

Since no external force acts on the system of the two masses, the center of mass of the system remains at rest.

Let the distance moved by the mass $2M$ be $d_1$ and the distance moved by the mass $5M$ be $d_2$.

From the conservation of the position of the center of mass:

$m_1 d_1 = m_2 d_2$

Substituting the given values $m_1 = 2M$, $m_2 = 5M$, and $d_1 = y$:

$2M y = 5M d_2$

$d_2 = \dfrac{2y}{5}$

The distance covered by the mass $5M$ is $\dfrac{2y}{5}$.

Answer: $\dfrac{2y}{5}$