1. **State the problem:** Calculate the product of 13 and 5. 2. **Formula used:** Multiplication of two numbers $a$ and $b$ is given by $a \times b$. 3. **Apply the formula:** Here, $a=13$ and $b=5$, so we calculate $13 \times 5$. 4. **Intermediate work:** $$ 13 \times 5 = 65 $$ 5. **Explanation:** Multiplying 13 by 5 means adding 13 five times or 5 thirteen times, which results in 65. 6. **Final answer:** $$ \boxed{65} $$