Answer
$(0,-5)$ ... $(0,5)$
Work Step by Step
Observe that the denominator under $y^{2}$ is greater than under $x^{2}.$
$a=5, b=2.$
The major axis is along the $y$-Axis. By the corresponding theorem,
An equation of the ellipse with center at $(0,0),$
foci at $(0,-c)$ and $(0,c),$
and vertices at $(0,-a)$ and $(0,a)$ is
$\displaystyle \frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1\quad $ where $a \gt b \gt 0$ and $b^{2}=a^{2}-c^{2}$
So, the vertices are $(0,-5)$ and $(0,5)$
