Which equation has the graph that is a parabola with a vertex at 5,3

We can solve this using vertex form of a parabola:

In our case h=5 and k=3, these are coordinates of our vertex point. 
There is no way to find a without knowing any other coefficients.
When you start solving some equations to get the parameters you always end up with identity (example 25=25). This means that your equation has an infinite number of solutions. In other words, any a will give you a parabola with vertex at the specified point.
The final answer would:

Where a is any real number.