Clearly, the foci (0, ±5) lie on y-axis.
∴ The equation of ellipse in standard form is

x2

a2

+

y2

b2

= 1
Now, vertices are (0, ±13) ⇒ a = 13, foci are (0, ±5) ⇒ c = 5
Also, we know that c2 = a2–b2
∴ (5)2 = (13)2–b2 ⇒ b2 = 169 – 25 = 144.
Hence the required equation of ellipse is

x2

144

+

y2

169

= 1