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.