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$sin(\frac{5\pi }{12}) = sin(\frac{\pi }{6}+\frac{\pi }{4}) = sin(\frac{\pi }{6}).cos(\frac{\pi }{4})+cos(\frac{\pi }{6}).sin(\frac{\pi }{4}) = \frac{1}{2}.\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2}.\frac{\sqrt{2}}{2} = \frac{\sqrt{2}+\sqrt{6}}{4}$

$cos(\frac{5\pi }{12}) = cos(\frac{\pi }{6}+\frac{\pi }{4}) = cos(\frac{\pi }{6}).cos(\frac{\pi }{4})-sin(\frac{\pi }{6}).sin(\frac{\pi }{4}) = \frac{\sqrt{3}}{2}.\frac{\sqrt{2}}{2}-\frac{1}{2}.\frac{\sqrt{2}}{2} = \frac{\sqrt{6}-\sqrt{2}}{4}$

$tan(\frac{5\pi }{12}) = \frac{sin(\frac{5\pi }{12})}{cos(\frac{5\pi }{12})} = \frac{\frac{\sqrt{2}+\sqrt{6}}{4}}{\frac{\sqrt{6}-\sqrt{2}}{4}}=\frac{\sqrt{6}+\sqrt{2}}{\sqrt{6}-\sqrt{2}}$

$sin(-555^{o}) = sin(720^{o}-555^{o}) = sin165^{o} = sin(180^{o}-165^{o}) = sin15^{o} = sin(45^{o}-30^{o})= sin(45^{o}).cos(30^{o})-cos(45^{o}).sin(30^{o}) = \frac{\sqrt{2}}{2}.\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}.\frac{1}{2} = \frac{\sqrt{6}-\sqrt{2}}{4}$

$cos(-555^{o}) = cos(720^{o}-555^{o}) = cos165^{o} = -cos(180^{o}-165^{o}) = -cos15^{o} = -cos(45^{o}-30^{o})= -cos(45^{o}).cos(30^{o})-sin(45^{o}).sin(30^{o}) = -\frac{\sqrt{2}}{2}.\frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}.\frac{1}{2} = -\frac{\sqrt{6}+\sqrt{2}}{4}$

$tan(-555^{o}) = \frac{sin(-555^{o})}{cos(-555^{o})} = \frac{\frac{\sqrt{6}-\sqrt{2}}{4}}{-\frac{\sqrt{6}+\sqrt{2}}{4}}=\frac{-\sqrt{6}+\sqrt{2}}{\sqrt{6}+\sqrt{2}}$