5. In flood control and rescue operations, a depression near the river dike has experienced a pipe burst, with $x$ cubic meters of river water already rushing in, and water continues to flow in at a rate of $y$ cubic meters per minute. Now, a water extraction and plugging project needs to be carried out. If 1 water pump is used, it will take 30 minutes to pump out all the water and start construction; if 2 water pumps work simultaneously, it will take 10 minutes to pump out all the water and start construction. Due to the urgent situation, the command post requires that the water be pumped out within 5 minutes to immediately start construction. At least how many water pumps need to work simultaneously? Assume that each water pump has a pumping rate of $z$ cubic meters per minute ($z>0$).
5.4

Let at least $n$ water pumps be required. According to the problem, we have
$$
\left\{\begin{array}{l}
x+30 y=30 z, \\
x+10 y=20 z, \\
x+5 y=n \cdot 5 z .
\end{array}\right.
$$

From equations (1) and (2), we can solve for $x=15 z, y=0.5 z$.
Substituting into equation (3), we get
$15 z+0.5 z \leqslant 5 n z$, hence $n \geqslant 3.1$.
Since $n$ is a positive integer, the minimum value is $n=4$.
That is, at least 4 water pumps need to be organized to work simultaneously.