$\begin{array}{l}\dfrac{5.n!(5 -n)!}{5!} - \dfrac{2.n!(6 - n)!}{6!} = \dfrac{14.n!.(7-n)!}{7!}\\ \Leftrightarrow \dfrac{5.n!(5 -n)!}{5!} - \dfrac{2.n!(5 - n)!(6 - n)}{6!} = \dfrac{14.n!.(5-n)!(6 - n)(7-n)}{7!}\\ \Leftrightarrow \dfrac{5}{5!} - \dfrac{2.(6 - n)}{6!} = \dfrac{14.(6 - n)(7-n)}{7!}\end{array}$