I need to find the real solutions to a simple equation:

$\displaystyle \sqrt{x+5}=x$

$\displaystyle x+5=x^2$

$\displaystyle x^2-x-5=0$

$\displaystyle x=\frac{1\pm \sqrt{21}}{2}$

It seems that there should be two real solutions to the equation. However, I am told that the equation has only 1 real solution.