\(\dfrac{17}{5}:\dfrac{5}{7}-\dfrac{7}{5}:\dfrac{12}{5}=\dfrac{17}{5}\times\dfrac{7}{5}-\dfrac{7}{5}\times\dfrac{5}{12}\)
\(=\dfrac{7}{5}\times\left(\dfrac{17}{5}-\dfrac{5}{12}\right)=\dfrac{7}{5}\times\left(\dfrac{204}{60}-\dfrac{25}{60}\right)\)
\(=\dfrac{7}{5}\times\dfrac{179}{60}=\dfrac{1253}{300}\)