To simplify the expression:

$\frac{11!5!6!}{11!5!6!},$

observe that the numerator and denominator are identical. Therefore:

$\frac{11!5!6!}{11!5!6!} = 1.$

Final Answer:

$1$

Would you like me to provide further explanations on factorial properties or related concepts?

Here are some follow-up questions for practice:

1. What is $7!$, and how is it computed?
2. Simplify $\frac{9!}{8!}$.
3. Find the value of $\frac{5! + 6!}{5!}$.
4. Simplify $\frac{12!}{10! \cdot 2!}$.
5. How many trailing zeros are in $15!$?

Tip: When simplifying factorial expressions, cancel out common terms to simplify your calculations effectively.