### Instruction: Calculate $6!-5\cdot5!-5!$.### Response: I recognize that $6!$ and $5!$ are related, since $6!=6\cdot5!$.
I can use this to simplify the expression.
I rewrite $6!-5\cdot5!-5!$ as $6\cdot5!-5\cdot5!-5!$.
I factor out $5!$ from each term and get $(6-5-1)\cdot5!$.
I simplify the parentheses and get $0\cdot5!$.
I know that any number multiplied by zero is zero, so the final answer is $0$.