For the hands to be in a straight line but not together, they must be 30 minutes apart. At 7:00, the minute hand is at 12 and the hour hand is at 7, so they are 35 minutes apart. To be 30 minutes apart, the minute hand must gain 5 minutes on the hour hand. The minute hand gains 55 minutes in 60 minutes. It will gain 5 minutes in (60/55) * 5 = 60/11 = 5 5/11 minutes.