5. Given the sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ with the general terms $a_{n}=2^{n}, b_{n}=3 n+2$, arrange the common terms of $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ in ascending order to form a new sequence $\left\{c_{n}\right\}$. The general term of $\left\{c_{n}\right\}$ is $\qquad$.
5. $2^{2 n+1}$.

When $n=2 m+1$, $a_{n}=2^{2 m+1}=2[4]^{m}=2[3+1]^{m}=2[3 k+1]=3 \cdot 2 k+2=b_{2 k}$ is a common term; when $n=2 m$, $a_{n}=2^{2 m}=4^{m}=[3+1]^{m}=3 k+1$ is not a common term. $c_{n}=a_{2 n+1}=2^{2 n+1}$.