Solve quadratic equation by completing the square.

Rewrite the equation as $x^2 + 8x = -5$. Complete the square by adding $(8/2)^2 = 16$ to both sides: $x^2 + 8x + 16 = -5 + 16$, which simplifies to $(x+4)^2 = 11$. Taking the square root of both sides gives $x+4 = \pm\sqrt{11}$, so $x = -4 \pm\sqrt{11}$.