To evaluate the expression for the inverse cosine of \(-\frac{\sqrt{3}}{2}\), we can reframe the problem as finding the angle whose cosine value equals \(-\frac{\sqrt{3}}{2}\). When dealing with inverse trigonometric functions, it's essential to remember the range of the angles. For the inverse cosine function, the angles are restricted to the interval \([0, \pi]\).

Within this interval, cosine values are positive in the first quadrant (from \(0\) to \(\frac{\pi}{2}\)) and negative in the second quadrant (from \(\frac{\pi}{2}\) to \(\pi\)). Since we are looking for a negative cosine value, we can conclude that the angle must be in the second quadrant.

Next, we identify the specific angle where the cosine equals \(-\frac{\sqrt{3}}{2}\). The angle that satisfies this condition is \(\frac{5\pi}{6}\), as the cosine of \(\frac{5\pi}{6}\) indeed equals \(-\frac{\sqrt{3}}{2}\). Therefore, the solution to the expression is:

\( \cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) = \frac{5\pi}{6} \)