1. **State the problem:** We are given the statement $5 \mid 8$ and asked to analyze it. 2. **Understand the notation:** The symbol $a \mid b$ means "$a$ divides $b$", i.e., $b$ is divisible by $a$ without remainder. 3. **Check divisibility:** To check if $5$ divides $8$, we perform the division: $$\frac{8}{5} = 1.6$$ Since $1.6$ is not an integer, $5$ does not divide $8$. 4. **Conclusion:** The statement $5 \mid 8$ is false because $8$ is not divisible by $5$. 5. **Additional note:** The set notation $\{8\} \in \mathbb{N}$ means the set containing $8$ is an element of the natural numbers, which is true since $8$ is a natural number. **Final answer:** $5 \nmid 8$ (5 does not divide 8).