Solve the following equation.

x5x+10+75x2+17x+70=5x+7\displaystyle \frac{{{x}-{5}}}{{{x}+{10}}}+\frac{{75}}{{{x}^{{2}}+{17}{x}+{70}}}=\frac{{5}}{{{x}+{7}}}


x=\displaystyle {x}=  
(Enter solution as a simplified fraction.)