Find the exact value of tan((5pi)/6)

$$\\tan(\frac{5\pi}{6})\\\\
=-tan(2\pi\;-\;\frac{5\pi}{6})\\\\
=-tan(\frac{\pi}{6})\\\\
=-tan 30^0\\\\
=\frac{-1}{\sqrt3}\\\\
=\frac{-\sqrt3}{3}\\\\$$

I assume you are working in radians (and not degrees)    -0.57735026919

The exact value   =    -1 / √3   or  -√3 / 3   .....{ if you prefer to "rationaloze" the denominator }.......