1. **State the problem:** Find the distance between the points $(-6,5)$ and $(-3,7)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ This formula comes from the Pythagorean theorem, where the difference in $x$ and $y$ coordinates form the legs of a right triangle. 3. **Calculate differences:** $$x_2 - x_1 = -3 - (-6) = -3 + 6 = 3$$ $$y_2 - y_1 = 7 - 5 = 2$$ 4. **Substitute into the formula:** $$d = \sqrt{3^2 + 2^2} = \sqrt{9 + 4} = \sqrt{13}$$ 5. **Simplify:** The distance between the points is $\sqrt{13}$, which is already in simplest radical form. **Final answer:** $$\boxed{\sqrt{13}}$$