1. **State the problem:** We are given the function $g(x) = a(x + 3)^2 - 5$ and the graph of $g$ with vertex at $(-3, -5)$ and passing through the point $(0, -1)$. We need to find the value of $a$. 2. **Recall the vertex form of a parabola:** The vertex form is $g(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Here, $h = -3$ and $k = -5$. 3. **Use the given point to find $a$:** Substitute $x = 0$ and $g(0) = -1$ into the equation: $$-1 = a(0 + 3)^2 - 5$$ 4. **Simplify the equation:** $$-1 = a(3)^2 - 5$$ $$-1 = 9a - 5$$ 5. **Solve for $a$:** Add 5 to both sides: $$-1 + 5 = 9a$$ $$4 = 9a$$ Divide both sides by 9: $$a = \frac{4}{9}$$ 6. **Final answer:** The value of $a$ is $\boxed{\frac{4}{9}}$ which corresponds to option D.