The problem asks to find the equation of a circle with center $(-2, 5)$ and radius $8$.

1. Problem Description

The problem asks to find the equation of a circle with center $(-2, 5)$ and radius $8$.

2. Solution Steps

The general equation of a circle with center $(h, k)$ and radius $r$ is given by:

$(x - h)^2 + (y - k)^2 = r^2$

In this problem, the center is $(-2, 5)$, so $h = -2$ and $k = 5$. The radius is $r = 8$.

Substituting these values into the general equation, we get:

$(x - (-2))^2 + (y - 5)^2 = 8^2$

$(x + 2)^2 + (y - 5)^2 = 64$

3. Final Answer

$(x + 2)^2 + (y - 5)^2 = 64$