Cos 5pi/3 is equals to cos 300 and since it is in quadrant 4 in the rule of All Student Take Calculus (All+,S=sin,T=tangent, andC=cos) it suppose to be a positive number and there is an instant trick to this if cos has an odd number in front you can basically add up to the 2nd digit so in this case it will be 30 but since its and odd number at 1st digit u should change cos to sin and the result is equivalent to sin 30 which is 1/2