Let $$t$$ be the time taken for the two masses to collide and $${x_{5M,}}\,{x_M}$$ be the distance travelled by the mass $$5M$$ and $$M$$ respectively.

The gravitational force acting between two sphere when the distance between them (12R - x) where x is a variable,

$$F = {{GM \times 5M} \over {{{\left( {12R - x} \right)}^2}}}$$

Acceleration of mass M, $${a_M} = {{G \times 5M} \over {{{\left( {12R - x} \right)}^2}}}$$

Acceleration of mass 5M, $${a_{5M}} = {{GM} \over {{{\left( {12R - x} \right)}^2}}}$$

For mass $$5M$$

$$u = 0,\,\,S = {x_{5M}},\,\,t = t,\,\,a{ = a_{5M}}$$

$$S = ut + {1 \over 2}a{t^2}$$

$$\therefore$$ $${x_{5M}} = {1 \over 2}{a_{5M}}{t^2}\,\,\,\,\,\,\,\,\,\,...\left( {i} \right)$$

For mass $$M$$

$$u = 0,\,\,s = {x_M},\,\,t = t,\,\,a = {a_M}$$

$$\therefore$$ $$s = ut + {1 \over 2}a{t^2} \Rightarrow $$

$${x_M} = {1 \over 2}{a_M}{t^2}\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$$

Dividing $$(ii)$$ by $$(iii)$$

$${{{x_{5M}}} \over {{x_M}}} = {{{1 \over 2}{a_5}_M{t^2}} \over {{1 \over 2}{a_M}{t^2}}}$$

$$ = {{{a_{5M}}} \over {{a_M}}} = {1 \over 5}$$

$$\therefore$$ $$5{x_{5M}} = {x_M}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left....( {iii} \right)$$

From the figure,

$${x_{5M}} + {x_M} = 12R - 2R - R = 9R\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( iv \right)$$

From $$(iii)$$ and $$(iv)$$

$${{{x_M}} \over 5} + {x_M} = 9R$$

$$\therefore$$ $$6{x_M} = 45R$$

$$\therefore$$ $${x_M} = {{45} \over 6}R = 7.5R$$

So two sphere collide when the sphere of mass M covered the distance of 7.5R.