To find the value of \( x \) in the equation
\[ 13^5 \times x = 13^{12}, \]
we can isolate \( x \) by dividing both sides by \( 13^5 \):
\[ x = \frac{13^{12}}{13^5}. \]
Using the properties of exponents, specifically \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify the right side:
\[ x = 13^{12 - 5} = 13^7. \]
Thus, the value of \( x \) that satisfies the equation is
\[ \boxed{13^7}. \]