#### Answer

False

#### Work Step by Step

We multiply the two expressions using the distributive property to check the answer:
$(5+\sqrt 3)(-5-\sqrt 3)$
=$5(-5-\sqrt 3)+\sqrt 3(-5-\sqrt 3)$
=$-25-5\sqrt 3-5\sqrt 3-\sqrt 3\sqrt 3$
=$-25-10\sqrt 3-\sqrt 3\sqrt 3$
=$-25-10\sqrt 3-(\sqrt 3)^{2}$
=$-25-10\sqrt 3-3$
=$-25-3-10\sqrt 3$
=$-28-10\sqrt 3$
Thus, the question statement is false.