1. **Stating the problem:** Given two numbers $a = 5$ and $b = 7$, find the sum $a + b$. 2. **Formula used:** The sum of two numbers is given by the formula: $$a + b$$ 3. **Explanation:** To find the sum, simply add the values of $a$ and $b$. 4. **Intermediate work:** $$5 + 7 = 12$$ 5. **Final answer:** The sum of $a$ and $b$ is $12$. This is a straightforward addition problem where you combine the two given values to get the result.