#### Answer

$x^{2}-2x-15=0$

#### Work Step by Step

Solution set is $\{-3,5\}$
$x=-3$ or $x=5$
$x+3=0$ or $x-5 = 0$
If $x+3=0$ or $x-5 = 0$ then
$(x+3)(x-5)=0$
$x^{2}+3x-5x-15=0$
$x^{2}-2x-15=0$
This is the required quadratic equation whose solution set is $\{-3,5\}$