At what angle are the hands of a clock inclined at 15 minutes past 5?

Problem restatement
Compute the smaller angle between the hands at 5:15.

Given data

• Hour-hand position at time H:M = 30H + 0.5M (degrees from 12).
• Minute-hand position at time H:M = 6M (degrees from 12).

Concept/Approach
Use angle = |(30H + 0.5M) − 6M| = |30H − 5.5M|.

Step-by-step calculation
Angle = |30×5 − 5.5×15| = |150 − 82.5| = 67.5°

Verification/Alternative
Hour hand at 5:15 is 150° + 7.5° = 157.5°. Minute hand is 15×6° = 90°. Difference = 67.5°.

Final Answer
67.5°