5. Let there be $n$ real numbers $x_{1}, x_{2}, \cdots, x_{n}$ satisfying: $\left|x_{1}\right|$ $<1(i=1,2, \cdots, n)$, and $\left|x_{1}\right|+\left|x_{2}\right|+\cdots+\left|x_{n}\right|$ $=19+\left|x_{1}+x_{2}+\cdots+x_{n}\right|$. Then the minimum value of $n$ is
5. 20 (Hint:

From $\left|x_{i}\right|<1(i=1,2, \cdots, n)$, it is easy to know that $19 \leqslant\left|x_{1}\right|+\left|x_{2}\right|+\cdots$ $+\left|x_{n}\right|<n$. When $n=20$, we have
$$
x_{i}=\left\{\begin{array}{l}
0.95(i=1,3, \cdots, 19), \\
-0.95(i=2,4, \cdots, 20)
\end{array}\right.
$$

satisfying the conditions of the problem.)