2015 AMC 12B Problem 8

Since $625 = 5^4,$ we have $$\begin{gathered} 625^{\log_5 2015} = 5^{4\log_5 2015} \\ = \left(5^{\log_5 2015}\right)^4 = 2015^4. \end{gathered}$$ Taking the fourth root gives $\left(2015^4\right)^{\frac{1}{4}} = 2015.$ Thus, the correct answer is D.