We have equation of hyperbola
$25 x^{2}-9 y^{2} =225$
$\Rightarrow \frac{x^{2}}{9}-\frac{y^{2}}{25}=1$
On comparing with $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1,$ we get
$a^{2} =9, b^{2}=25$
$\therefore $ Eccentricity, $e =\sqrt{1+\frac{b^{2}}{a^{2}}}$
$=\sqrt{1+\frac{25}{9}}$
$=\frac{\sqrt{34}}{3}$