Find the root of \( \sqrt[5]{-3125} \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sqrt[5]{-3125}=\square \) (Simplify your answer.) B. The root is not a real number.

We start with the expression: \[ \sqrt[5]{-3125} \] Since the index \(5\) is odd, the \(5\)th root of a negative number is also negative. In other words, we have: \[ \sqrt[5]{-3125} = -\sqrt[5]{3125} \] Next, we simplify \(\sqrt[5]{3125}\). Notice that: \[ 3125 = 5^5 \] Thus, we can write: \[ \sqrt[5]{3125} = \sqrt[5]{5^5} = 5 \] Substituting this back, we get: \[ \sqrt[5]{-3125} = -5 \] So, the correct choice is: A. \(\sqrt[5]{-3125}=-5\)