Choice A is the correct answer.

1. The vertex is $(3, 5)$, so the minimum y-value is 5.
2. Since it opens upward, the graph goes up to infinity from 5.
3. Therefore, the range is all y-values greater than or equal to 5 ($y \geq 5$).

Choice B is incorrect because that would be for a parabola opening downward. Choice C is incorrect because it uses the x-coordinate. Choice D is incorrect because the range of a quadratic is never all real numbers (the domain is).