Proving a multiplicative group module n is generated in a handy way

Question

Prove that $(\mathbb{Z}/23\mathbb{Z})^*$ is generated by $5\pmod{23}$

Is there a tactic or theorem that could help me finding the power of $5\pmod{23}$ for each element?

I was thinking about using Euler's theorem or Fermat's Little theorem, but I don't see how they could help me get for example $4\pmod{23}$ as generated by $5\pmod{23}$.

Thanks in advance

Answer 1

You can check that $5^{11} \ne 1 \pmod{23}$ and $5^{2}\ne 1 \pmod{23}$ using exponentiation by squaring.