These problems can be solved with a system of equations. With each point given, we can write an equation y = ab^x and plug in the values of x and y. This will give us two equations with two variables which we can solve for.

With the point (0,5), we know that when x is 0, y is 5:

Y = ab^x

5 = ab^0

Because we are given a point at which x = 0, we can see here that we already know a = 5.

Now with the point (3,5000):

Y = ab^x

5000 = (5)(b)^3

Solve for b:

b = 10

Finally, we can state the exponential function:

Y = 5(10)^x

You can check this answer by plugging in the x and y values into this equation.