Prove $5\mid2^{4n}-1$ by induction 
For all $n\ge1$, use mathematical induction to establish each other the following divisibility statements:
  $$5\mid2^{4n}-1$$ 

I was wondering if someone could help me with the set up of this proof. I only have done proofs with mathematical induction when I am given a series of numbers and I can incorporate my induction hypothesis in for one of my terms in the series. 
Step by step explanation please?

Since you asked for a set-up,


*

*Show the statement is true for $n=1$, i.e.


$$5 \ \Big| \ 2^4-1$$


*

*Let $n\in\mathbb{N}$ be fixed. Assume for all $k<n$ that


$$5 \ \Big| \ 2^{4k}-1$$
Show that 
$$5 \ \Big| \ 2^{4n}-1$$
