Find the domain of $f(x)=\sqrt{\log_{0.4}(\frac{x-1}{x+5})}$.

(1, ∞)

$f(x)=\sqrt{\log_{0.4}(\frac{x-1}{x+5})}$

exists if

$\log_{0.4}(\frac{x-1}{x+5})≥0$ and $(\frac{x-1}{x+5})>0$

or $\frac{x-1}{x+5}≤(0.4)^0$ and $\frac{x-1}{x+5}>0$

or $\frac{x-1}{x+5}≤1$ and $\frac{x-1}{x+5}>0$

or $\frac{x-1}{x+5}-1≤0$ and $\frac{x-1}{x+5}>0$

or $\frac{6}{x+5}≤0$ and $\frac{x-1}{x+5}>0$

or $x+5>0$ and $\frac{x-1}{x+5}>0$

or $x>-5$ and $x-1>0$

or $x>-5$ and $x>1$

Thus, the domain f(x) is $(1, ∞)$.