At what time between 5 and 5 : 30 is the hands of a clock 5 min apart?

At 5 O' clock, the minute hand is 25 min space apart. The two hands will be 5 min apart between 5 and 5 : 30, if the minute hand is (25 - 5) i.e, 20 min spaces behind the hour hand.
Now, 55 min are gained in 60 min.
20 min are gained in = (60/55 x 20) = (240/11) = 21⁹/₁₁ min
So, the hands will be 5 min apart at 21⁹/₁₁ min past 5.