Cracking secret key, n, and m by hand with the Diffie-Hellman key exchange brute force

Problem: You see Michael and Nikita agree on a secret key using the Diffie-Hellman key exchange. Michael and Nikita choose $p = 97$ and $g = 5$. Nikita chooses a random number n and tells Michael that $g^n \equiv 3\pmod{97}$, and Michael chooses a random number $m$ and tells Nikita that $g^m ≡ 7 \pmod{97}$. Brute force crack their code: What is the secret key that Nikita and Michael agree upon? What is $n$? What is $m$?

This is how the Diffie-Hellman exchange is defined in the textbook:

1. Together Michael and Nikita choose a 200-digit integer p that is likely to be prime, and choose a number $g$ with $1 < g < p$.
2. Nikita secretly chooses an integer $n$.
3. Michael secretly chooses an integer $m$.
4. Nikita computes $g^n \pmod{p}$ on her handheld computer and tells Michael the resulting number over the phone.
5. Michael tells Nikita $g^m \pmod{p}$.
6. The shared secret key is then $s\equiv g^{nm}\pmod{p}$ which both Nikita and Michael can compute.

My thoughts/attempts:
Attempt 1. I tried to find $n$ through solving the modular equation $5^n\equiv 3\pmod{97}.$ Then we have $n\equiv \log_53\pmod{97},$ which is not an integer and thus doesn't make sense.
Attempt 2. I tried to find the key using $g^n$ and $g^m.$ However, I don't see a way to reach $g^{nm}$ since $g^ng^m = g^{n+m},$ and we cannot calculate $(g^n)^m$ or $(g^m)^n$ without knowing $m$ or $n,$ which from Attempt 1 I can't find integers for.

Would appreciate help! Thank you