Question 5
Find all possible three-digit numbers $\overline{abc}$ such that $\overline{abc}=a!+b!+c!$. (Note: $n!$ (read as $n$ factorial) means $n!=n\times(n-1)\times(n-2)\times\cdots\times3\times2\times1$. For example, $6!=6\times5\times4\times3\times2\times1=720$.)