5. A pool is equipped with 5 water pipes numbered (1), (2), (3), (4), (5), some of which are inlet pipes and some are outlet pipes. If two pipes are opened simultaneously, the time to fill the pool is as follows:
\begin{tabular}{|c|c|c|c|c|c|}
\hline Pipes opened & (1)(2) & (2)(3) & (3)(4) & (4)(3) & (5)(1) \\
\hline Time to fill the pool (hours) & 2 & 15 & 6 & 3 & 10 \\
\hline
\end{tabular}

Then, the pipe number that can fill the pool the fastest when opened alone is
(A) (1);
(B) (2);
(C) (4);
(D) (3) or (5).
5. (C)

Solution Let the flow rate of the pipe numbered $i$ per hour be $Q_{i}\left(i=1,2,3,4,5, Q_{i}Q_{3}, Q_{2}Q_{1}, Q_{5}Q_{2}>Q_{5}>Q_{3}, \quad Q_{4}>Q_{1}>Q_{3}\right)$.
It is also easy to see that there must be a positive value among $Q_{i}$, with $Q_{4}$ being the largest, so opening the pipe numbered 4 alone will take the shortest time to fill the pool.