You're right, f(0) = 5 and 0 is in the domain.
Choice A is incorrect, as it does not include 5.
The answer is A, which makes no sense to me.
I sketched the graph to find that the maximum y-value occurs when x = 0. that is, y = 5 when x = 0. Since, in the domain, 0 has a square bracket, I assumed that the graph did meet x = 0, and thus also met y = 5. The minimum is at x = .785, and my calculator tells it it also meets that. So I figured the single round bracket on the domain had no effect, has it has nothing to do with the range, and the range would be [2,5].
But it's not, and I just can't grasp why.