I'm guessing your limit is
[tex]\displaystyle \lim_{x\to5} \frac{-\sin\left(\frac{\pi x}3\right)}3[/tex]
The limand is continuous at x = 5, so we can evaluate the limit directly by substituting x = 5:
[tex]\displaystyle \lim_{x\to5} \frac{-\sin\left(\frac{\pi x}3\right)}3 = -\frac13 \sin\left(\frac{5\pi}3\right) = -\frac13 \times \left(-\frac{\sqrt3}2\right) = \boxed{\frac1{2\sqrt3}} = \boxed{\frac{\sqrt3}6}[/tex]
