Step 1 :
Coordinates of vertices and foci are $(0, \pm 3 )$ and foci $(0, \pm 5)$ respectively.
Clearly the vertices are on the y - axis.
Hence the equation of the hyperbola is of the form $ \large\frac{y^2}{a^2}$$ - \large\frac{x^2}{b^2}$$=1$
Since the vertices are $(0, \pm 3)$
$ \therefore a = 3$
Since the foci are $(0, \pm 5) \Rightarrow c = 5$
$ \therefore c^2 = a^2+b^2$
$ \Rightarrow b^2 = 25-9$
$ = 16$
Hence the equation of the hyperbola is
$ \large\frac{y^2}{9}$$ - \large\frac{x^2}{16}$$=1$