\({a_{slipping}} = g\sin \theta \,\,\,\,\,\,\,...\left( i \right)\)

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

\({a_{rolling}} = \frac{{g\sin \theta }}{{1 + \frac{{{k^2}}}{{{R^2}}}}} = \frac{{g\sin \theta }}{{1 + \frac{2}{5}}}\)

\(\left( {For\,solid\,sphere,\frac{{{k^2}}}{{{R^2}}} = \frac{2}{5}} \right)\)

\(= \frac{5}{7}g\sin \theta \,\,\,\,\,...\left( {ii} \right)\)

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

\(\frac{{{a_{rolling}}}}{{{a_{slipping}}}} = \frac{5}{7}\)