To do this you first have to find the measure of the angle that is inside that pie-shaped part of the circle. The measure around the circle is 360 which is the same as 2pi. Subtract 5pi/3 from 2pi and you get pi/3, which happens to be a 60 degree angle. What you are looking for is arc length (not arc measure which is measured in degrees, not inches, feet, etc.) The formula for that is this:
, where beta is the arc measure in question and d is the diameter of the circle. If the central angle we found measured 60 degrees, then the arc it intercepts also measures 60 degrees, therefore s measures 300 (360-60). So now our formula looks like this:
. When you do all that math, multiplying pi in, you get an arc length of 47.1, the first choice.