To solve the expression \(\frac{7^x}{7^5} = 7^{12}\), we can use the properties of exponents.
According to the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can rewrite the left side:
\[ \frac{7^x}{7^5} = 7^{x-5} \]
Now, we set this equal to the right side:
\[ 7^{x-5} = 7^{12} \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x - 5 = 12 \]
Now, we solve for \(x\):
\[ x = 12 + 5 = 17 \]
Therefore, the missing number is \(17\).