1. **State the problem:** Find the exact distance between points $A(-3,1)$ and $B(5,6)$ on the coordinate plane. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Apply the formula:** Substitute $x_1 = -3$, $y_1 = 1$, $x_2 = 5$, and $y_2 = 6$: $$d = \sqrt{(5 - (-3))^2 + (6 - 1)^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(5 + 3)^2 + (5)^2}$$ $$d = \sqrt{8^2 + 5^2}$$ 5. **Calculate squares:** $$d = \sqrt{64 + 25}$$ 6. **Add the values:** $$d = \sqrt{89}$$ 7. **Final answer:** The exact distance between points $A$ and $B$ is $$\boxed{\sqrt{89}}$$.