1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula for a circle's equation:** The standard form is $$ (x - h)^2 + (y - k)^2 = r^2 $$ where $(h, k)$ is the center and $r$ is the radius. 3. **Identify the center and radius:** The center is $(-4, 3)$ and the radius is $5$ units. 4. **Substitute the values into the formula:** $$ (x - (-4))^2 + (y - 3)^2 = 5^2 $$ which simplifies to $$ (x + 4)^2 + (y - 3)^2 = 25 $$ 5. **Final answer:** The equation of the circle is $$ (x + 4)^2 + (y - 3)^2 = 25 $$ This equation represents all points $(x, y)$ that are exactly 5 units away from the center $(-4, 3)$ on the coordinate plane.