1. **State the problem:** We are given a rectangle with an area of 15 cm². The height is 5 cm and the width is given as $q - 2$ cm. We need to find the value of $q$. 2. **Formula for the area of a rectangle:** $$\text{Area} = \text{height} \times \text{width}$$ 3. **Apply the formula:** $$15 = 5 \times (q - 2)$$ 4. **Simplify the equation:** $$15 = 5q - 10$$ 5. **Isolate $q$:** Add 10 to both sides: $$15 + 10 = 5q - 10 + 10$$ $$25 = 5q$$ 6. **Divide both sides by 5:** $$\frac{25}{\cancel{5}} = \frac{5q}{\cancel{5}}$$ $$5 = q$$ 7. **Final answer:** The value of $q$ is $5$ cm.