This is the easiest, non-technical, method:

_{(I'm on Snow Leopard, I've edited these to match Mavericks - the exact buttons to click may be wrong)}

1. Open Calendar.app
2. Make a new event today for 00:00
3. Set it to repeat every day
4. Alert should be Open file. Select Other > Find iTunes in Applications
5. Make an Applescript and type this: tell application "iTunes" to quit. Save it somewhere
6. Make another event tomorrow for 05:00
7. Set it to repeat every day
8. Alert should be Open file. Select Other > the applescript you made above

Done!

This is the easiest, non-technical, method:

_{(I'm on Snow Leopard, I've edited these to match Mavericks - the exact buttons to click may be wrong)}

1. Make an Applescript and type this: tell application "iTunes" to activate
2. Open Calendar.app
3. Make a new event today for 00:00
4. Set it to repeat every day
5. Alert should be Open file. Select Other > find the applescript you just made
6. Make an Applescript and type this: tell application "iTunes" to quit. Save it somewhere
7. Make another event tomorrow for 05:00
8. Set it to repeat every day
9. Alert should be Open file. Select Other > find the applescript you just made

Done!

The calendar app does not have to be running to allow the events to take place.