To solve the equation:
\[ \frac{7^x}{7^5} = 7^{12} \]
we can use the properties of exponents. When you divide exponential terms with the same base, you subtract the exponents:
\[ 7^{x - 5} = 7^{12} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x - 5 = 12 \]
Solving for \(x\):
\[ x = 12 + 5 \] \[ x = 17 \]
So, the solution is:
\[ \boxed{17} \]