#### Answer

$15-5\sqrt {15}+3\sqrt 6-3\sqrt {10}$

#### Work Step by Step

$(5+\sqrt 6)(3-\sqrt {15})$
=$5(3-\sqrt {15})+\sqrt 6(3-\sqrt {15})$
=$15-5\sqrt {15}+3\sqrt 6-(\sqrt 6\sqrt {15})$
=$15-5\sqrt {15}+3\sqrt 6-\sqrt {6\times15}$
=$15-5\sqrt {15}+3\sqrt 6-\sqrt {90}$
=$15-5\sqrt {15}+3\sqrt 6-\sqrt {9\times10}$
=$15-5\sqrt {15}+3\sqrt 6-(\sqrt 9\times\sqrt {10})$
=$15-5\sqrt {15}+3\sqrt 6-3\sqrt {10}$