Solve. \[ \begin{array}{l}\sqrt[3]{5 x-3}=-2 \\ \text { A. The solution(s) is/are the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) } \\ \text { B. There is no solution. }\end{array} \text { ? } \]

To solve the equation \(\sqrt[3]{5x-3}=-2\), we first cube both sides to eliminate the cube root: \[ 5x - 3 = (-2)^3 \] Calculating the right side gives us: \[ 5x - 3 = -8 \] Next, we add 3 to both sides: \[ 5x = -8 + 3 \] \[ 5x = -5 \] Now, divide both sides by 5: \[ x = -1 \] So, the solution is \(x = -1\). In response to the choices presented: **A. The solution(s) is/are -1.** There's no need for choice B since we found a valid solution!