1. **State the problem:** Find the distance between the points $(6,5)$ and $(7,8)$. 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. **Substitute the values:** $$d = \sqrt{(7 - 6)^2 + (8 - 5)^2}$$ 4. **Calculate the differences:** $$d = \sqrt{1^2 + 3^2}$$ 5. **Square the differences:** $$d = \sqrt{1 + 9}$$ 6. **Add the squares:** $$d = \sqrt{10}$$ 7. **Final answer:** The distance between the points is $$\sqrt{10}$$ units.