Answer
$\{7\}$
Work Step by Step
Step 1. Given the equation $\sqrt {x-3}+5=x, x\geq3$, rewrite the equation as $\sqrt {x-3}=x-5$. Take square on both sides to get $x-3=x^2-10x+25$ or $x^2-11x+28=0$ which can be factored as $(x-4)(x-7)=0$
Step 2. Solve the above equation to get $x= 7$ (discard $x=4$ as it is not an answer) or in set form as $\{7\}$
