1. **State the problem:** We have a right-angled triangle ABC with angle B = 90°. 2. **Given:** Hypotenuse AC = 13 cm, one leg BC = 5 cm. 3. **Find:** The length of the other leg AB. 4. **Use the Pythagorean theorem:** In a right triangle, $AC^2 = AB^2 + BC^2$. 5. **Substitute the known values:** $$13^2 = AB^2 + 5^2$$ 6. **Calculate squares:** $$169 = AB^2 + 25$$ 7. **Isolate $AB^2$:** $$AB^2 = 169 - 25 = 144$$ 8. **Find $AB$ by taking the square root:** $$AB = \sqrt{144} = 12$$ **Final answer:** The length of side AB is 12 cm.