2. In the Cartesian coordinate system $x O y$, if the asymptotes of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>0, b>0)$ do not intersect the circle $x^{2}+y^{2}-$ $6 y+5=0$, then the range of the eccentricity of the hyperbola is $\qquad$.
2. $\left(1, \frac{3}{2}\right)$.

From the problem, we know that the distance from the center of the circle $(0,3)$ to the asymptote is greater than 2, i.e., $\frac{3 a}{\sqrt{a^{2}+b^{2}}}>2$.
Therefore, the eccentricity of the hyperbola $e \in\left(1, \frac{3}{2}\right)$.