5. There are 10 people with distinct heights standing in a row, and each person is either taller or shorter than the person in front of them. The number of arrangements that meet this condition is $\qquad$ (answer with a number).

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5. There are 10 people with distinct heights standing in a row, and each person is either taller or shorter than the person in front of them. The number of arrangements that meet this condition is $\qquad$ (answer with a number).
5.512.

According to the problem, the person standing in the last position must be the tallest or the shortest. Otherwise, there would be people both taller and shorter than the 10th person, which contradicts the given conditions. Therefore, there are two ways to arrange the 10th position.

Let the number of arrangements for 10 people be $a_{10}$. After arranging the 10th position, there are $a_{9}$ ways to arrange the first 9 positions. Thus, we have
$$
\left\{\begin{array}{l}
a_{10}=2 a_{9} \\
a_{1}=1 .
\end{array}\right.
$$

By analogy, $a_{1}, a_{2}, \cdots, a_{9}, a_{10}$ form a geometric sequence with a common ratio $q=2$, so $a_{10}=a_{1} q^{9}=2^{9}=512$.