#### Answer

$31-19\sqrt{3}$

#### Work Step by Step

Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ then
\begin{array}{l}\require{cancel}
(2-\sqrt{3})(5-7\sqrt{3})
\\\\=
2(5)+2(-7\sqrt{3})-\sqrt{3}(5)-\sqrt{3}(-7\sqrt{3})
\\\\=
10-14\sqrt{3}-5\sqrt{3}+7(3)
\\\\=
10-14\sqrt{3}-5\sqrt{3}+21
\\\\=
31-19\sqrt{3}
.\end{array}