1. **State the problem:** We are given the volume of a cube as 125 cubic units and need to find the edge length. 2. **Formula:** The volume $V$ of a cube with edge length $s$ is given by: $$V = s^3$$ 3. **Apply the formula:** Substitute $V = 125$: $$125 = s^3$$ 4. **Solve for $s$:** Take the cube root of both sides: $$s = \sqrt[3]{125}$$ 5. **Evaluate the cube root:** Since $125 = 5^3$, we have: $$s = 5$$ 6. **Answer:** The edge length of the cube is 5 units.