To find the minimum of the graph described by the equation \( y = (x+4)^2 - 5 \), we can first identify the vertex of the parabola since this is a quadratic function in vertex form.
The vertex form of a quadratic function is given by:
\[ y = a(x-h)^2 + k \]
where \((h, k)\) is the vertex. In your equation, \( a = 1 \), \( h = -4 \), and \( k = -5 \).
Thus, the vertex of the parabola is at the point \((-4, -5)\).
Since the coefficient \( a \) is positive (1), the parabola opens upwards, meaning the vertex is indeed the minimum point on the graph.
Therefore, the minimum of the graph \( y = (x + 4)^2 - 5 \) is at the point:
\[ \boxed{(-4, -5)} \]
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