Proof by Induction Divisibility. $6^n-5n+4$ is divisible by 5 for all positive integers $n$.
$n >=1$

Prove By Induction
My attempt is as follows:

$n=1$
  $6^1-5(1) +4$
  $=5$, Therefore 5 is divisible by 5 so $n=1$ is true
  
  Assume its true for $n=k$
  consider $n=k+1$
  $6^k-5k+4=5.x$
I am stuck here would appreciate some assistance.


Assume $6^n+5n+4$ is multiple of $5$.
Let us consider $$6^{n+1}-5(n+1)+4=(5+1)6^n-5n-5+4=5(6^n-1)+(6^n-5n+4)$$
The first summand is multiple of $5$  and the second is multiple of $5$ by inductive assumtion.
