5. Let $0<a<1$. If $x_{1}=a, x_{2}=a^{x_{1}}, x_{3}=a^{x_{2}}, x_{4}$ $=a^{x_{3}}, \cdots, x_{n}=a^{x_{n}-1}, \cdots$, then the sequence $\left\{x_{n}\right\}(\quad$.
(A) increasing
(B) odd terms increase, even terms decrease
(C) decreasing
(D) even terms increase, odd terms decrease
5.B.
(1) $x_{1}=a^{1}, x_{2}=a^{x_{1}}$, since $1>a$, then $a^{1}a^{x_{1}}$. Therefore, $a^{1}a^{0}=1$, so $x_{2}>x_{4}$.
By analogy, we get $x_{2}>x_{4}>x_{6} \cdots$.
Thus, the sequence $\left\{x_{n}\right\}$ has increasing odd terms and decreasing even terms.