The angle between the hour and minute hands of a clock at 5:10 can be calculated using the following approach:

Step 1: Calculate the position of the hour hand

Each hour on the clock represents an angle of 30 degrees (since $360^\circ / 12 = 30^\circ$ per hour). At exactly 5:00, the hour hand is at: $5 \times 30^\circ = 150^\circ$

However, at 5:10, the hour hand has moved slightly ahead because it's not exactly at 5:00. The hour hand moves 0.5 degrees per minute (since $30^\circ / 60 = 0.5^\circ$ per minute). So in 10 minutes, the hour hand moves: $10 \times 0.5^\circ = 5^\circ$ Thus, the position of the hour hand at 5:10 is: $150^\circ + 5^\circ = 155^\circ$

Step 2: Calculate the position of the minute hand

Each minute represents an angle of 6 degrees (since $360^\circ / 60 = 6^\circ$). At 10 minutes, the minute hand is at: $10 \times 6^\circ = 60^\circ$

Step 3: Calculate the angle between the two hands

The angle between the hour and minute hands is the absolute difference between their positions: $| 155^\circ - 60^\circ | = 95^\circ$

So, the angle at 5:10 is 95 degrees.

Would you like more details or have any questions about the calculation?

Here are 5 related questions for further exploration:

1. What is the angle between the hands at 7:25?
2. How do you calculate the angle between the hands at any given time?
3. What is the reflex angle at 5:10?
4. How would the angle change at 5:20?
5. What is the smallest angle between the hands at 4:45?

Tip: The minute hand moves 6 degrees per minute, while the hour hand moves 0.5 degrees per minute.