Acceleration of the solid sphere slipping down the incline without rolling is

${a_{slipping}} = g\sin \theta$       ....(i)

Acceleration of the solid sphere rolling down the incline without slipping is

${a_{rolling}} = {{g\sin \theta } \over {1 + {{{k^2}} \over {{R^2}}}}} = {{g\sin \theta } \over {1 + {2 \over 5}}}$
$\left( \because{For\,\,solid\,\,sphere,{{{k^2}} \over {{R^2}}} = {2 \over 5}} \right)$

= ${5 \over 7}g\sin \theta$   ... (ii)

Divide eqn. (ii) by eqn. (i), we get

${{{a_{rolling}}} \over {{a_{slipping}}}} = {5 \over 7}$