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're new to induction, I'll give the framework and let you fill in the details. The induction step goes something like this:
Suppose that $5| 2^{4n} - 1$, and write $5k = 2^{4n} - 1$. Then
\begin{align*}
2^{4(n + 1)} - 1 &= 2^{4n} \cdot 2^4 - 1 \\
&= (5k + 1) \cdot 16 - 1 \\
&= 5k + 16 - 1
\end{align*}
Can you finish it from here, justifying each step?
