\[\left( 5\sqrt{3} - \sqrt{27} \right) \cdot \sqrt{3} =\]
\[= 5\sqrt{3} \cdot \sqrt{3} - \sqrt{27} \cdot \sqrt{3} = 5 \cdot 3 - \sqrt{81} =\]
\[= 15 - 9 = 6\]