Solve the equation
$$
\left[\frac{5+6 x}{8}\right]=\frac{15 x-7}{5} .
$$
Let $\frac{15 x-7}{5}=y$, then $x=\frac{5 y+7}{15}$. Substituting into the original equation, we get
- $\left[\frac{10 y+39}{40}\right]=y$.
We have $0 \leqslant-\frac{10 y+39}{40}-y<1$.
Solving, we get $-\frac{1}{30}<y \leqslant \frac{39}{30}$.
But $y$ is an integer, so $y=0$ or 1. Solving for $x$, we get $x=\frac{7}{15}$ or $\frac{4}{5}$.