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)}

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.

You can also run EDITOR=nano crontab -e and add lines like this:

0 0 * * * open -a itunes
0 5 * * * osascript -e 'quit app "itunes"'