1. **State the problem:** We are given a circle with center $(-2, 7)$ and radius $\sqrt{5}$. We need to write the equation of the circle in standard form and describe its graph. 2. **Formula for the equation of a circle:** The standard form of a circle's equation with center $(h, k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. **Substitute the given values:** Here, $h = -2$, $k = 7$, and $r = \sqrt{5}$. Substitute these into the formula: $$ (x - (-2))^2 + (y - 7)^2 = (\sqrt{5})^2 $$ 4. **Simplify the equation:** $$ (x + 2)^2 + (y - 7)^2 = 5 $$ 5. **Graph description:** The graph is a circle centered at $(-2, 7)$ with radius $\sqrt{5}$. This means every point on the circle is exactly $\sqrt{5}$ units away from the center. **Final answer:** $$ (x + 2)^2 + (y - 7)^2 = 5 $$