Answer
$\{5\}$
Work Step by Step
Step 1. Given the equation $\sqrt {x+4}+\sqrt {x-1}=5, x\geq1$, rewrite the equation as $\sqrt {x+4}=5-\sqrt {x-1}$. Take square on both sides to get $x+4=25+x-1-10\sqrt {x-1}$ or $\sqrt {x-1}=2$
Step 2. Solve the above equation to get $x= 5$ or in set form as $\{5\}$
