Hi I'm having some trouble with big O notation. I know how to do the simple ones but this is above my head. Any help would be appreciated.

Show using only the definition of O(f) that:

1) 5^n is O(n!)

2)n! is not O(5^n)

I know that 5^n<=n! for n=12 but I don't know how to show this. The book says to use induction 'but I don't know how and for 2 as well. Any ideas?

Thanks in advance.