What is the cosine of negative five pi over six?

Cosine has a period of 2pi. So
cos(-5pi/6)
=cos(-5pi/6+2pi)
=cos(7pi/6)
=-cos(7pi/6-pi)
=-cos(pi/6)
=-sqrt(3)/2

Note that each step has a justification, but we are not allowed to give u r l references, so cannot provide you with more information.