13.384 Five people perform a certain job. The first, second, and third, working together, can complete the entire job in 327.5 hours; the first, third, and fifth together - in 5 hours; the first, third, and fourth together - in 6 hours; and the second, fourth, and fifth together - in 4 hours. In what time interval will all 5 people complete this job, working together?
Solution. Let $x_{i}$ be the productivity of the $i$-th worker, $y$ be the volume of work. Then, according to the problem,

$$
\left\{\begin{array}{l}
x_{1}+x_{2}+x_{3}=\frac{y}{7.5} \\
x_{1}+x_{3}+x_{5}=\frac{y}{5} \\
x_{1}+x_{3}+x_{4}=\frac{y}{6} \\
x_{2}+x_{4}+x_{5}=\frac{y}{4}
\end{array}\right.
$$

Multiplying the last equation by 2 and then adding all four equations, we get: $3\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}\right)=y\left(\frac{1}{7.5}+\frac{1}{5}+\frac{1}{6}+\frac{1}{2}\right) \Rightarrow \frac{y}{x_{1}+x_{2}+x_{3}+x_{4}+x_{5}}=3$.

Answer: in 3 hours.