\(\left(x-1\right)^5=\frac{1}{32}\)
\(\Leftrightarrow\left(x-1\right)^5=\frac{1}{2^5}\)
\(\Leftrightarrow\left(x-1\right)^5=\left(\frac{1}{2}\right)^5\)
\(\Leftrightarrow x-1=\frac{1}{2}\)
\(\Leftrightarrow x=\frac{1}{2}+1\)
\(\Leftrightarrow x=\frac{3}{2}\)