Answer
$(0,-5)$ and $(0,5)$.
Work Step by Step
The equation of the ellipse here has the form $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$, where $a\gt b\gt0$, the vertices are at $(0,-a)$ and $(0,a)$. $a=\sqrt{25}=5$, hence the vertices are at $(0,-5)$ and $(0,5)$.
