At 15 minutes past 5 o' clock, the minute hand is at 3
and hour hand is slightly ahead of 5.

In 60 minutes, the hour hand moves ahead by 300
∴ In 15 minutes, the hour hand moves ahead by = (30/60)*15
= 7.5°

Angle between 3 and 5 hour spaces = 60°.
∴ The total angle between the two hands at
 15 minutes past 5 o' clock = 60 + 7.5 = 67.5°