1. **Stating the problem:** Calculate the factorial of a number, for example, 5!. 2. **Formula:** The factorial of a positive integer $n$ is defined as: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 3. **Important rules:** - Factorial is only defined for non-negative integers. - By definition, $0! = 1$. 4. **Calculate 5!:** $$5! = 5 \times 4 \times 3 \times 2 \times 1$$ 5. **Intermediate steps:** $$5! = 5 \times 4 = 20$$ $$20 \times 3 = 60$$ $$60 \times 2 = 120$$ $$120 \times 1 = 120$$ 6. **Final answer:** $$5! = 120$$ So, the factorial of 5 is 120.