Rewrite the expression by factoring out \( (x-5) \). \( 5 x^{2}(x-5)-7(x-5) \)

To rewrite the expression by factoring out \( (x-5) \), we can first observe that both terms in the expression \( 5 x^{2}(x-5)-7(x-5) \) share the common factor \( (x-5) \). Thus, we can factor this out: \[ (x-5) \left( 5x^{2} - 7 \right). \] So, the expression simplifies to: \[ (x-5) (5x^{2} - 7). \]