Angle traced by hour hand in 21/4 hrs. = (360/12x21/4)°
= 157½°
Angle traced by min.hand in 15 min = (360/60x15)°
= 90°
Therefore, the Required angle = [(157½°)-90°]
= 67½°

Its better to use formula as it can save lots of time in exams. However we should understand
the basics for sure. Please find the method given below to solve the same problem in
the traditional way.
15 minutes past 5 = 5 hour 15 minutes = 51560 hour=514 hour = 214 hour
Angle traced by hour hand in 12 hours = 360°
Hence Angle traced by hour hand in 214 hour=36012×214=30×214=30×5.25=157.5°
Angle traced by minute hand in 60 minutes = 360°
Angle traced by minute hand in 15 minutes = 36060×15=90°
Required angle = 157.5 - 90 = 67.5°