Choice A is the correct answer. Use the method of completing the square.

1. Take half of $b=6$, which is 3. Square it: $3^2 = 9$.
2. Add and subtract 9: $y = (x^2 + 6x + 9) - 9 + 5$.
3. Factor the perfect square trinomial: $y = (x + 3)^2 - 4$.

The vertex is $(-3, -4)$.

Choice B is incorrect because it forgets to subtract the 9 that was added. Choice C is incorrect because the sign inside the parenthesis is wrong (should be +). Choice D is incorrect because it uses 6 instead of half of 6.