To solve the equation
\[ \frac{5^x}{5^5} = 5^{12}, \]
we can apply the properties of exponents. Recall that when we divide two powers with the same base, we subtract the exponents:
\[ \frac{5^a}{5^b} = 5^{a-b}. \]
Using this property, we rewrite the left side of the equation:
\[ 5^{x - 5} = 5^{12}. \]
Since the bases are the same, we can set the exponents equal to each other:
\[ x - 5 = 12. \]
Now, to solve for \( x \), we add 5 to both sides:
\[ x = 12 + 5, \]
which simplifies to
\[ x = 17. \]
Thus, the value of \( x \) that makes the equation true is
\[ \boxed{17}. \]