automate app launch at midnight ?
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)


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