discrete mathematics - Proving that $5^n - 1$ is divisible by $4$ by mathematical induction.

I have done it, but I am not sure that the inductive step is right. Can anybody please clear me about it?

Basic steps as:

Taking $n=1$: $p(1)=5-1=4$.

Inductive hypothesis: Assume the statement is true for $p(k)$. $5^k - 1$ is divisible by $4$.

Inductive steps: We must show $p(k+1)$ is true when $p(k)$ is true. $$\begin{align*} & 5^k -1 + 5^{k+1} -1\\ & 5^k -1 + 5.5^{k} -1\\ & (5^k -1) + 4 \end{align*}$$