To ask "what is the true time ?" in this situation is the same as to ask:
  

     At what time between 2:00 pm  and 3:00 pm the angle between the minute and the hour hands is exactly 30 degrees ?  

         ( 30 degrees  correspond to 5 minutes, 1/12 of the full revolution of the minute hand )


And the answer to it is the solution of this equation:

 = 30.        (! 6t is the angular position of the minute hand measured in degrees from the "vertical up" position;
                            ( (60 + (6/12)*t) is the position of the hour hand measured in degrees from the "vertical up" position).


Or, which is the same,

 = 30.

Simplify and solve:

60 - 0.5t - 6t = 30  ====>  5.5t = 60 - 30  ====>  5.5t = 30  ====>

t =  = 5.(45) = 5 minutes and 27.(27) seconds = 5 minutes and 27.(27) seconds (approximately).


Here the record 5.(45)  means 5 followed periodical decimal fraction with the period 45;
                27.(27) means 27 followed periodical decimal fraction with the period 27.