#### Answer

no solution

#### Work Step by Step

Separate the square roots on two sides. Then square both sides and combine like terms. When down to the last square root, square both sides again to solve. Since no real numbers can make the square root equal to $-1$, there is no solution.
$\sqrt {x-5}-\sqrt {x-8}=3$
$\sqrt {x-5}=3+\sqrt {x-8}$
$(\sqrt {x-5})^2=(3+\sqrt {x-8})^2$
$x-5=9+6\sqrt {x-8}+x-8$
$-6=6\sqrt {x-8}$
$\sqrt {x-8}=-1$
no solution