Well, my first thought is that 10 shift registers probably won't be enough to drive 5000 LEDs :
Chase lights can be fun. With an Arduino, you can do lots of varied patterns and speeds. Or make a "Knight Rider" bar that gradually fades the leading and trailing LEDs to make a really fluid-looking movement.
Make bars or matrices of 24, 60, and 60 LEDs, and turn on one LED per second/minute to show the time in graphic form.
If you have a long hallway, make several "light fixtures" of 10 or 20 LEDs apiece, and distribute them down the hall. Put an Arduino with a Ping sensor at one end of the hall, and use it to figure out where you are, and turn on only the nearest light(s).
Put LEDs all over your car, and use the Arduino to animate them so you look like UFO (or a carnival ride ;D) going down the street.
Mount them around your patio, and make them "dance" in time to the music when you have a party.