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$5tg^3(-\frac{10}{3}\pi )+ctg(-\frac{19\pi }{6})=5tg^3(-3\pi -\frac{\pi }{3})+ctg(-3\pi -\frac{\pi}{6})=\\\\=-5tg^3\frac{\pi}{3}-ctg\frac{\pi}{6}=-5\cdot (\sqrt3)^3-\sqrt3=-5\cdot 3\cdot \sqrt3-\sqrt3=-16\sqrt3\\\\\\\star \; \; tg(-3\pi -\frac{\pi }{3})=tg(-(3\pi +\frac{\pi}{3})\, )=-tg(3\pi +\frac{\pi}{3})=-tg\frac{\pi}{3}\\\\tg^3(-3\pi -\frac{\pi}{3})=(-tg\frac{\pi}{3})^3=-tg^3 \frac{\pi}{3}=(-\sqrt3)^3=-3\sqrt3\\\\ctg(-3\pi -\frac{\pi}{6})=-ctg(3\pi +\frac{\pi}{6})=-ctg\frac{\pi}{6}\; \; \star$