Answer
$7$
Work Step by Step
$\sqrt {x-3} +5=x \implies (\sqrt {x-3})^2=(x-5)^2$
Re-arrange as: $ x^2 -10x +25 -(x-3) =0$
$\implies x^2-11x+28=0$
$\implies x(x-7)-4(x-7)=0$
or, $(x-4)(x-7)=0$
So, $ x=7,4$
Neglect the negative term of $ x=4$, because it does not belong to the domain of the variable; so we have $ x=7$
