To simplify the expression \((24^2)^5\) using the Power Rule of Exponents, we use the rule which states that \((a^m)^n = a^{m \cdot n}\).
Applying this to our expression:
\[ (24^2)^5 = 24^{2 \cdot 5} = 24^{10} \]
Thus, the expression simplifies to \(24^{10}\).
The correct response from the options given is:
\(24\) to the \(10\)th power.