1. **State the problem:** We need to find the equation of a circle given its center and radius. 2. **Recall the formula for the equation of a circle:** The standard form of a circle's equation 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 from the problem:** The center is given as $(-5, 3)$ and the radius is $3$. 4. **Substitute the values into the formula:** $$ (x - (-5))^2 + (y - 3)^2 = 3^2 $$ which simplifies to $$ (x + 5)^2 + (y - 3)^2 = 9 $$ 5. **Final answer:** The equation of the circle is: $$ (x + 5)^2 + (y - 3)^2 = 9 $$ This equation represents a circle centered at $(-5, 3)$ with radius $3$.