5. (1999 National High School Mathematics League Question) Given a geometric sequence $\left\{a_{n}\right\}$ with a common ratio of $q(q \neq 1)$, set $b_{1}=a_{1}+$ $a_{2}+a_{3}, b_{2}=a_{4}+a_{5}+a_{6}, \cdots, b_{n}=a_{3 n-2}+a_{3 n-1}+a_{3 n}, \cdots$, then the sequence $\left\{b_{n}\right\} \quad$ ～）
A. is an arithmetic sequence
B. is a geometric sequence with a common ratio of $q$
C. is a geometric sequence with a common ratio of $q^{3}$
D. is neither an arithmetic sequence nor a geometric sequence
5. Choose C. $=\frac{a_{1} q^{3 n}\left(1+q+q^{2}\right)}{a_{1} q^{3 n-3}\left(1+q+q^{2}\right)}=q^{3}$, so $\left\{b_{n}\right\}$ is a geometric sequence with a common ratio of $q^{3}$.