Answer
$157$
Work Step by Step
The number of gorillas is given as follows
$$
2 \pi \int_{0}^{5} r \rho(r) d r=\int_{0}^{5} \frac{104 \pi r}{\left(1+r^{2}\right)^{2}}dr\\
=\int_{0}^{5} 104 \pi r \left(1+r^{2}\right)^{-2}dr=-\left.\frac{52 \pi}{1+r^{2}}\right|_{0} ^{5}=50 \pi\approx 157.
$$
