\(\frac{11}{125}-\frac{17}{18}-\frac{5}{7}+\frac{4}{9}+\frac{17}{14}\)
\(=\frac{11}{125}+\left(\frac{-17}{18}+\frac{4}{8}\right)+\left(\frac{-5}{7}+\frac{17}{14}\right)\)
\(=11+\left(\frac{-17}{18}+\frac{8}{18}\right)+\left(\frac{-10}{14}+\frac{17}{14}\right)\)
\(=\frac{11}{125}+\left(\frac{-9}{18}\right)+\frac{7}{14}\)
\(=\frac{11}{125}+\left(\frac{-1}{2}+\frac{1}{2}\right)\)
\(=\frac{11}{125}+0\)
\(=\frac{11}{125}\)