cathodes connected to an common resistor
If you do that, the LED brightness will vary as you light up more LEDs. In fact, one LED alone will be bright, and then the LEDs will get dimmer as you switch on more of them. There's no shortcut; use one resistor per LED in this sort of application. You can use a SIL or DIL resistor array pack, as shown, or you can use surface-mount resistors. They're not as difficult to solder as people say!http://www.flickr.com/photos/anachrocomputer/2910132542
For others who are reading this: avoid connecting LEDs in parallel, because the variations in forward voltage between one LED and the next will cause brightness variations. LEDs in series can work well if the power supply voltage is high enough, but won't gain you very much at 5V. Always install the resistor(s), even if your LED seems to work without one, because otherwise excessive current will flow and that can burn out the LED rather quickly!