At 5:00, hour hand is at 150 degrees. For a right angle (90 degrees apart), the minute hand should be at 150+90=240 degrees from 12. Minute hand position at m minutes past 5 is 6m degrees. Setting up: minute hand gains 5.5 degrees per minute on hour hand. At 5:00 they are 150 degrees apart. Need 90 degrees: 150−5.5m=90, so m=5.560=11120=101110 (before 5:30, not in range). For 90 degrees with minute ahead: 5.5m−150=90, m=5.5240=11480=43117.