The "Energy Saver" panel in System Preferences allows the user to schedule wake ups. The only problem is is that the most frequent it allows for this to happen is ONCE per day. Is there any way or any tool or any software that can make it wake up at any custom interval? I'm running Mac OS X 10.5.8.
This app seems to be the solution to your problem. http://www.ibeezz.com/en/
Haven't tested it myself though.
This article, How to Power On Your Mac at a Specific Date and Time, shows how to schedule your Mac to power on using Energy Saver,
pmset, and Power Manager.
The most capable method is with Power Manager; it can schedule the multiple power on and wake up events you need using the Graphical User Interface (GUI).
Power Manager supports Mac OS X 10.6 and later, but the previous version is still available and supports Mac OS X 10.4 - 10.7 for PPC and Intel.
Disclosure: I work for the company who makes Power Manager.