Prove that for all $n\ge9$, there exist natural numbers $x,y$ such that $n=2x+5y$. How would you use induction to prove this? 

Are you including zero as a natural number?  I think it has to be to get 10
since  9 = 2 x 2 + 1 x 5
we can always make another 1 to add on with 5 - 2x2.  If the number is even it can always be 2x, so to make the next odd number we can always take 2 from x and add set y = 1, for ever
