1. **State the problem:** We need to find the surface area of a cube where each edge length is given as $AB = 5$ mm. 2. **Formula for surface area of a cube:** The surface area $S$ of a cube with side length $a$ is given by $$S = 6a^2$$ This is because a cube has 6 faces, each a square with area $a^2$. 3. **Calculate the area of one face:** $$a^2 = 5^2 = 25 \text{ mm}^2$$ 4. **Calculate total surface area:** $$S = 6 \times 25 = 150 \text{ mm}^2$$ 5. **Interpretation:** The cube's surface area is the sum of the areas of all 6 congruent square faces, each with area 25 mm², resulting in a total surface area of 150 mm². **Final answer:** $$\boxed{150 \text{ mm}^2}$$