\(\frac{5}{6}+\frac{1}{12}+\frac{2}{3}+\frac{2}{7}+\frac{1}{25}+\frac{1}{4}-\frac{5}{42}\)
\(=\left(\frac{5}{6}+\frac{2}{7}-\frac{5}{42}\right)+\left(\frac{1}{12}+\frac{2}{3}+\frac{1}{4}\right)+\frac{1}{25}\)
\(=\left(\frac{35}{42}+\frac{12}{42}-\frac{5}{42}\right)+\left(\frac{1}{12}+\frac{8}{12}+\frac{3}{12}\right)+\frac{1}{25}\)
\(=\frac{42}{42}+\frac{12}{12}+\frac{1}{25}=1+1+\frac{1}{25}=2\frac{1}{25}\)