At what point does the terminal side of the angle 5π/6 in standard position intersect the unit circle?

The angle of 5π/6 is 150 degree. start from the positive side of the x axis, rotate counterclockwise for 150 degree, the terminal side is in the second quadrant, forming a 30 degree angle with the negative side of the x axis. This 30 degree angle is what we need to focus on. 
Draw a vertical line from your terminal point straight down to the negative side of the x axis, and draw another line from the terminal point to the center of the unit circle. Now you have a right triangle.
In a unit circle, the radius, that is, the hypotenuse of of this right triangle, is always 1.
sin30=y:r =1/2, so y is 1/2
cos30=x:r=√3/2, so x is √3/2
because the terminal point is in the second quadrant, x is negative, y is positive, therefore, the standard position of the intersection is at (-√3/2, 1/2)