1. **State the problem:** Simplify the expression $\frac{5!}{(5-3)!}$. 2. **Recall the factorial definition:** For any positive integer $n$, $n! = n \times (n-1) \times (n-2) \times \cdots \times 1$. Also, $0! = 1$. 3. **Calculate the denominator:** $5 - 3 = 2$, so the denominator is $2! = 2 \times 1 = 2$. 4. **Calculate the numerator:** $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. 5. **Substitute values:** $\frac{5!}{(5-3)!} = \frac{120}{2}$. 6. **Simplify the fraction:** $\frac{120}{2} = 60$. 7. **Final answer:** $60$