Answer
$15,250 \ gallons$
Work Step by Step
Let $V$ be the volume of the reservoir. Therefore,
$\dfrac{dV}{dt}=3000+20 t$
At the initial point, the reservoir is empty.
So, $V(0)=0$ and $dV=(3000+20 t) \ dt$
Integrate the above equation to obtain:
$\int_0^5 dV=\int_0^5 (3000+20 t) \ dt$
$\implies V(5)=[3000t+10t^2]_0^5$
$\implies V(5)=[3000(5)+10(5^2)]-[3000(0)+10(0)]$
$\implies V(5)=15, 250 \ gallons$
Therefore, the quantity of water in the reservoir after five hours is $15, 250 \ gallons$