Let's simplify the expression step by step.
The expression given is:
\[ 5^2 \times \frac{5^6}{5^{-6}} \]
First, we can simplify the fraction \(\frac{5^6}{5^{-6}}\) by using the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\):
\[ \frac{5^6}{5^{-6}} = 5^{6 - (-6)} = 5^{6 + 6} = 5^{12} \]
Now we substitute this back into the original expression:
\[ 5^2 \times 5^{12} \]
Next, we can combine the powers of 5 using the property of exponents \(a^m \times a^n = a^{m+n}\):
\[ 5^2 \times 5^{12} = 5^{2 + 12} = 5^{14} \]
Therefore, the expression simplifies to:
\[ 5^{14} \]
Now, we can check the multiple-choice answers. The only expression that matches this is:
\[ 5^{14} \]
So, the final answer is:
\[ \boxed{5^{14}} \]