[Math] How to prove $5^n − 1$ is divisible by 4, for each integer n ≥ 0 by mathematical induction

Question

Definition of Divisibility
Let n and d be integers and d≠0
then d|n ⇔ $\exists$ an integer k such that n=dk"

Source: Discrete Mathematics with Applications, Susanna S. Epp

Prove the following statement by mathematical induction.
$5^n − 1$ is divisible by 4, for each integer n ≥ 0.

My attempt:

Let the given statement p(n).

(1) $5^0 − 1=1-1=0$ is divisible by 4. So p(0) is true.

(2) Suppose that for all integers $k \ge 0$, p(k) is true, so $5^k − 1$ is divisible by 4 by inductive hypothesis.

Then we must show that p(k+1) is true.

$5^{k+1} − 1$ = $5\cdot 5^k − 1$

I can't further develop the step. I'm stuck on this step.
It should be something like $5\cdot(5^k − 1)$ so that p(k+1) be true to apply inductive hypothesis.

Answer 1

Hint:

$$5^{k+1}-1=5\times(5^k-1)+4$$