1. **State the problem:** We need to find the perimeter of rhombus ABCD with vertices A(1,1), B(-2,-3), C(-5,1), and D(-2,5). 2. **Recall the properties of a rhombus:** All sides are equal in length. So, we only need to find the length of one side and multiply by 4. 3. **Use the distance formula:** The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.$$ 4. **Calculate the length of side AB:** $$AB = \sqrt{(-2 - 1)^2 + (-3 - 1)^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.$$ 5. **Since all sides are equal, the perimeter $P$ is:** $$P = 4 \times AB = 4 \times 5 = 20.$$ **Final answer:** The perimeter of rhombus ABCD is 20 units.