Question 140712
I think you mean {{{1 + sqrt(5-x)=x-2}}}  (if so, next time construct it like this 1 + sqrt(5 - x) = x - 2)


Add -1 to both sides:


{{{sqrt(5-x)=x-3}}}


Square both sides (this introduces the possibility of an extraneous root -- check your answers carefully)


{{{5-x=(x-3)^2}}}
{{{5-x=x^2-6x+9}}}
{{{-x^2+6x-x-9+5=0}}}
{{{-x^2+5x-4=0}}}
{{{x^2-5x+4=0}}}


Solve by any method.  Remember to check for and exclude extraneous roots.


Hint: {{{sqrt(4)=2<>-2}}}, {{{-sqrt(4)=-2}}}