\(\frac{17}{19}+\left(\frac{13}{5}-\frac{5}{6}\right)-\left(\frac{1}{6}-\frac{2}{19}\right)=\frac{17}{19}+\frac{13}{5}-\frac{5}{6}-\frac{1}{6}+\frac{2}{19}\)
\(=\frac{13}{5}+\left(\frac{17}{19}+\frac{2}{19}\right)+\left(-\frac{5}{6}-\frac{1}{6}\right)\)
\(=\frac{13}{5}+1-1=\frac{13}{5}\)