Answer
Foci: $(0,2+\sqrt{11})$ and $(0,2-\sqrt{11})$.
Work Step by Step
$\displaystyle \frac{(x-0)^{2}}{25}+\frac{(y-2)^{2}}{36}=1$
(major axis vertical),
$a^{2}=36,$
$a=6$
$b^{2}=25$,
$b=5$
Center: $(h,k)=(0, 2)$
$c^{2}=a^{2}-b^{2}=36-25=11$
$c=\sqrt{11}\approx 3.317$
Foci are $c$ units above and $c$ units below the center.
Foci: $(0,2+\sqrt{11})$ and $(0,2-\sqrt{11})$.