1. Given the sequences $\left\{a_{n}\right\}$ and $\left\{b_{n}\right\}$ satisfy
$$
a_{n}=2^{\frac{2 n+3}{5}}, b_{n}=\frac{1}{n} \log _{2}\left(a_{1} a_{2} \cdots a_{n}\right)\left(n \in \mathbf{N}_{+}\right) \text {. }
$$

Then the general term formula of the sequence $\left\{b_{n}\right\}$ is
1. $b_{n}=\frac{n+4}{5}$.

From $a_{n}=2^{\frac{2 n+3}{5}}$, we get
$a_{1} a_{2} \cdots a_{n}=2^{\frac{2(1+2+\cdots+n)+3 n}{s}}=2^{\frac{n(n+4)}{s}}$.
Therefore, $b_{n}=\frac{1}{n} \cdot \frac{n(n+4)}{5}=\frac{n+4}{5}$.