Factor out the GCF: \[ 10 x^{3}-15 x \]

Step 1 ：Identify the Greatest Common Factor (GCF) of the terms in the expression \(10x^{3}-15x\). The GCF is \(5x\).

Step 2 ：Divide each term in the expression by the GCF to get the remaining factor. The remaining factor is \(10x^{2}-15\).

Step 3 ：Write the factored expression by multiplying the GCF and the remaining factor. The factored expression is \(x(10x^{2}-15)\).

Step 4 ：\(\boxed{x(10x^{2}-15)}\) is the final answer.