The given function is $f(x) = (x + 4)^2 + 5$.

Step-by-Step Solution:

1. Identify the function type:
   This is a quadratic function of the form $f(x) = a(x + h)^2 + k$, which represents a parabola. The parabola opens upwards because the coefficient of $(x + 4)^2$ is positive (1).

2. Find the vertex:
   The vertex of a parabola in the form $(x + h)^2 + k$ is at $(-h, k)$. Here, $h = -4$ and $k = 5$.
   Therefore, the vertex is at $(-4, 5)$.

3. Determine the behavior:
   Since the parabola opens upwards, the function decreases to the left of the vertex and increases to the right of the vertex.

4. State the interval of decreasing:
   The graph is decreasing on the interval where $x < -4$.

Final Answer:

The function is decreasing on the interval $(-\infty, -4)$.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. Find the interval where the function $f(x) = (x - 3)^2 + 2$ is increasing.
2. Determine the vertex of the function $f(x) = (x + 2)^2 - 1$.
3. What is the axis of symmetry for the function $f(x) = (x - 5)^2 + 3$?
4. Find the range of the function $f(x) = (x + 1)^2 - 4$.
5. Determine whether the function $f(x) = -2(x + 1)^2 + 5$ is increasing or decreasing.

Tip: The vertex of a quadratic function is the key point where the graph changes direction (increases or decreases).