1. **State the problem:** Find the distance between the points $(5, -4)$ and $(-1, 4)$. 2. **Formula:** 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:** $$d = \sqrt{(-1 - 5)^2 + (4 - (-4))^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(-6)^2 + (8)^2}$$ 5. **Square the numbers:** $$d = \sqrt{36 + 64}$$ 6. **Add the squares:** $$d = \sqrt{100}$$ 7. **Simplify the square root:** $$d = 10$$ **Final answer:** The distance between the points $(5, -4)$ and $(-1, 4)$ is $10$.