5. Solve the inequality $\frac{5 x^{2}}{x-1}>5 x+1$.
Solution: $\frac{5 x^{2}}{x-1}>5 x+1 ; \frac{5 x^{2}(5 x+1)(x-1)}{x-1}>0$,

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$\frac{5 x^{2}-5 x^{2}+4 x+1}{x-1}>0$. Answer: $x \in\left(-\infty ;-\frac{1}{4}\right) \cup(1 ;+\infty)$.