Answer
$\{ \frac{-1\pm\sqrt {85}}{2}\}$
Work Step by Step
Step 1. Use the relation $log_5y=2\rightarrow y=5^2$, we have $x^2+x+4=25$ or $x^2+x-21=0$
Step 2. Solve the equation $x=\frac{-1\pm\sqrt {1+4(21)}}{2}=\frac{-1\pm\sqrt {85}}{2}$
Step 3. Check answers $\{ \frac{-1\pm\sqrt {85}}{2}\}$ and they are good.
