The equation given is \( y = (x + 4)^2 - 5 \). This is in the vertex form of a quadratic equation, which is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola.
In this case, we have:
- \( h = -4 \) (since \( x + 4 \) can be rewritten as \( x - (-4) \))
- \( k = -5 \)
Since the coefficient of the squared term is positive (1 in this case), the parabola opens upwards, indicating that the vertex is the minimum point.
Thus, the minimum value of \( y \) occurs at the vertex, which is at the point \( (-4, -5) \).
Therefore, the minimum value of the graph is \( -5 \).