1. **State the problem:** Find the distance between the points $(-3,4)$ and $(5,1)$. 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 given points:** $$d = \sqrt{(5 - (-3))^2 + (1 - 4)^2}$$ 4. **Simplify inside the parentheses:** $$d = \sqrt{(5 + 3)^2 + (-3)^2}$$ $$d = \sqrt{8^2 + (-3)^2}$$ 5. **Calculate the squares:** $$d = \sqrt{64 + 9}$$ 6. **Add the values inside the square root:** $$d = \sqrt{73}$$ 7. **Final answer:** The distance between the points is $\sqrt{73}$ units.