As the gravitation provides the centripetal force
$\large\frac{mv^2}{r}=\frac{k}{r^{\frac{5}{2}}}$
$v^2=\large\frac{k}{mr^{\Large\frac{3}{2}}}$
$T=\large\frac{2 \pi r}{v}$$=2 \pi r \sqrt {\large\frac{mr^{\Large\frac{3}{2}}}{k}}$
$T^2=\large\frac{4 \pi^2 m}{k} $$r ^{\large\frac{7}{2}}$
$T^2 \; \alpha \; r^{\large\frac{+7}{2}}$
Hence a is the correct answer.