1. The problem is to calculate the factorial of 5, denoted as $5!$. 2. The factorial of a positive integer $n$ is the product of all positive integers from 1 to $n$. 3. The formula for factorial is: $$n! = n \times (n-1) \times (n-2) \times \cdots \times 2 \times 1$$ 4. Applying this to $5!$: $$5! = 5 \times 4 \times 3 \times 2 \times 1$$ 5. Calculate step-by-step: $$5! = 5 \times 4 \times 3 \times 2 \times 1 = 20 \times 3 \times 2 \times 1$$ $$= 60 \times 2 \times 1 = 120 \times 1 = 120$$ 6. Therefore, the value of $5!$ is $120$.