Step 1 :The question is asking for the equivalent expression of \(5^{10} \cdot 5^{5}\).
Step 2 :From the laws of exponents, we know that when multiplying two exponents with the same base, we add the exponents.
Step 3 :So, \(5^{10} \cdot 5^{5}\) is equivalent to \(5^{10+5}\).
Step 4 :Therefore, the expression equivalent to \(5^{10} \cdot 5^{5}\) is \(\boxed{5^{15}}\).