Solve for x. List your solutions, separated by commas (if there are multiple solutions). If there is no solution, enter DNE.

xx+55x+1=7x43x2+6x+5\displaystyle \frac{{x}}{{{x}+{5}}}-\frac{{5}}{{{x}+{1}}}=\frac{{{7}{x}-{43}}}{{{x}^{{2}}+{6}{x}+{5}}}

x =