Answer
$x=10$
Work Step by Step
Isolate the square root on one side. Then square both sides and put all terms on one side. Factor by trial and error to solve for $x$. One of the answers does not work.
$x-\sqrt {2x+5}=5$
$x=5+\sqrt {2x+5}$
$(x-5)^2=2x+5$
$x^2-10x+25=2x+5$
$x^2-12x+20=0$
$(x-2)(x-10)=0$
$x=2,10$
$2-\sqrt{2\times2+5}\ne5$
$x=10$
