5. Solve the inequality $\frac{4-x}{x-5}>\frac{1}{1-x}$.
Solution: $\frac{4-x}{x-5}+\frac{1}{x-1}>0 ; \frac{(4-x)(x-1)+x-5}{(x-5)(x-1)}>0$,

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$\frac{-x^{2}+6 x-9}{(x-5)(x-1)}>0, \frac{-(x-3)^{2}}{(x-1)(x-5)}>0$. Answer: $(1 ; 3) \cup(3 ; 5)$.