The coefficients of the $(r-1)^{th},r^{th}$ and $(r+1)^{th}$ terms in the expansion of $(x+1)^n$ are in the ratio of $1 : 3 : 5$. Find both $n$ and $r$.

Question

$\begin{array}{1 1}(A)\;n=7,r=3\\(B)\;n=3,r=7\\(C)\;n=4,r=8\\(D)\;n=5,r=3\end{array} $