Prime Number Identification: Analyzing Integer Properties

To solve this problem, we'll follow these steps:

• Step 1: Identify the given numbers: $8$, $4$, $5$, $12$.
• Step 2: Verify the primality of each number.

Now, let's work through each step:
Step 1: The numbers provided are $8$, $4$, $5$, $12$.
Step 2: We need to determine if each number is a prime by checking if they have divisors other than 1 and themselves:

• $8$ is divisible by $2$, so it has divisors besides 1 and 8. Therefore, 8 is not a prime number.
• $4$ is divisible by $2$, so it has divisors besides 1 and 4. Therefore, 4 is not a prime number.
• $5$ is not divisible by any integer other than 1 and 5. Thus, 5 is a prime number.
• $12$ is divisible by $2$ and $3$, so it has divisors besides 1 and 12. Therefore, 12 is not a prime number.

Therefore, the solution to the problem is $5$.