To simplify the expression \((24^2)^5\) using the Power Rule of Exponents, we apply the rule which states that \((a^m)^n = a^{m \cdot n}\).
In this case:
\[ (24^2)^5 = 24^{2 \cdot 5} = 24^{10} \]
Therefore, the simplified expression is:
24 to the 10th power