\lim_{x \to 3} \frac{ \sqrt{x-1}- \sqrt{5-x} }{x-3} = [0/0]=
= \lim_{x \to3} \frac{( \sqrt{x-1} - \sqrt{5-x} )( \sqrt{x-1} + \sqrt{5-x}) \sqrt{x-3} }{(x-3)( \sqrt{x-1}+ \sqrt{5-x} ) } =
= \lim_{x \to3} \frac{(2x-6) \sqrt{x-3} }{(x-3)( \sqrt{x-1}+ \sqrt{5-x} } =
= \lim_{x \to3} \frac{2 \sqrt{x-3} }{ 2\sqrt{2} }=0