For a right angle, the hands must be 15 minutes apart. At 5:30, the minute hand is at 6 and the hour hand is halfway between 5 and 6. They are 2.5 min spaces apart. To get to 15 min apart, the minute hand must gain 15-2.5=12.5 min. No, that's after 5. At 5:00 they are 25 min apart. We need them to be 15 min apart. Case 1: minute hand gains 10 min. Time = 10*(12/11) = 21 9/11 min. Case 2: minute hand gains 40 min. Time = 40*(12/11) = 43 7/11 min. The second case is between 5:30 and 6.