Why do this problem?
is a great context in which to apply knowledge of angles based on a full turn and it helps to consolidate analogue clock features too.
Having a large geared demonstration clock available would be a good idea to discuss this problem with the group.
Which is the minute hand and which is the hour hand?
How long does it take the hour hand do go a full circle ($360$ $^\circ$) round the clock?
How long does it take the minute hand do go a full circle round the clock?
How many degrees does the minute hand go through in one hour?
So many degrees does it go through in $15$ minutes? In $10$ minutes?
So, how many degrees does it go through in $5$ minutes?
Suggest doing this problem, Two Clocks
or possibly just exploring the interactivity to see how clocks move.