The standard form of the equation of the hyperbola,
They give you the vertices (0,4) and (0,0) and that it passes through the point (0, square root of 5)

You need to double check your problem, you can't have a hyperbola with vertices (0,4) and (0,0) that passes through point (0, \sqrt{5}) . I think the x value of your third point is a typo, or a mistake, or something. I'll keep an eye on this question.