a) \(\left(5-x\right)^3=-27\)
\(\Rightarrow\left(5+x\right)=\left(-3\right)^3\)
\(\Rightarrow5+x=-3\)
\(\Rightarrow x=-3-5\)
\(\Rightarrow x=-8\)
b) \(\left(1-x\right)^2=\dfrac{1}{9}\)
\(\Rightarrow\left(1-x\right)^2=\left(\dfrac{1}{3}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}1-x=\dfrac{1}{3}\\1-x=-\dfrac{1}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=1-\dfrac{1}{3}\\x=1+\dfrac{1}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{3}\\x=\dfrac{4}{3}\end{matrix}\right.\)
c) \(5^{3-x}=125\)
\(\Rightarrow5^{3-x}=5^3\)
\(\Rightarrow3-x=3\)
\(\Rightarrow x=3-3\)
\(\Rightarrow x=0\)