RGB LED matrix power too low?
It sure sounds like you've got a short from +5 to GND somewhere in that "smart LED" array. I don't think we can easily help you find it- you'll have to find it yourself. You can verify this with a multimeter set to ohms (with power off, of course). 

I suggest giving it a good visual once-over, and if that fails to turn up anything (it's possible one of the LEDs is internally shorted, but less likely) then start cutting the 5V lines into groups and test the groups individually. Divide and conquer (or do a binary search if you prefer programming paradigms to political strategies).  

I suggest disconnecting the Arduino during this testing- it can't help to have it connected, and it's possible you could damage something. 

The (rather sketchy) LED datasheet is mute on the quiescent current draw, but I would expect a small current draw at 5V with no controller connected- perhaps some hundreds of mA or less.