Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n

First I would do the base case (the first value):Test n=1,11¹-6=5. 5 is divisible by 5 therefore true for n=1.
Now we assume true for n=k,11^k-6 is divisible by 5.Next we test n=k+1,11^k+1-6We can rearrange this into 1111^k-6= 1011^k+11^k-6We know that for n=k the result is 11^k-6 which we assume to be true so that part can be assumed to be true.The first part can be factorised into 5(2*11^k) which is divisible by 5. Therefore we have shown that if true for n=k, true for n=k+1 and as we shown true for n=1 it must also be true for all natural numbers. So we have proved this through induction