smc

Since the product of the first $n$ numbers in the sequence is $n^2$, the product of the first $n+1$ numbers in the sequence is $(n+1{)}^2$. Therefore the $n+1$th number in the sequence is $\frac{(n+1{)}^2}{n^2}$. Therefore the third and the fifth numbers are $\frac{9}{4}$ and $\frac{25}{16}$ respectively. The sum of those numbers is $\frac{36}{16}+\frac{25}{16}=\boxed{\frac{61}{16}}$.