5. \((\sqrt{75}-\sqrt{27})\cdot\sqrt{3}\)

Упростим корни: \(\sqrt{75}=5\sqrt{3}\), \(\sqrt{27}=3\sqrt{3}\).

\((\sqrt{75}-\sqrt{27})\sqrt{3}=(5\sqrt{3}-3\sqrt{3})\sqrt{3}=2\sqrt{3}\cdot\sqrt{3}=2\cdot3=6\).

Ответ: 6