\(sinx+cosx=\frac{1}{5}\Rightarrow\left(sinx+cosx\right)^2=\frac{1}{25}\)
\(\Rightarrow1+2sinx.cosx=\frac{1}{25}\Rightarrow2sinx.cosx=-\frac{24}{25}\)
\(\Rightarrow4sinx.cosx=-\frac{48}{25}\)
\(\Rightarrow\left(sinx+cosx\right)^2-4sinx.cosx=\frac{1}{25}+\frac{48}{25}=\frac{49}{25}\)
\(\Rightarrow\left(sinx-cosx\right)^2=\frac{49}{25}\Rightarrow\left|sinx-cosx\right|=\frac{7}{5}\)