1. The problem asks for the cube root of $5^{15}$. 2. Recall the property of exponents and roots: the $n$th root of $a^m$ is $a^{\frac{m}{n}}$. 3. Applying this, the cube root of $5^{15}$ is $5^{\frac{15}{3}}$. 4. Simplify the exponent: $\frac{15}{3} = 5$. 5. So, the cube root of $5^{15}$ is $5^5$. 6. Calculate $5^5$: $5 \times 5 \times 5 \times 5 \times 5 = 3125$. 7. Therefore, the cube root of $5^{15}$ is $3125$. Final answer: 3125 (Option D).