I've seen a lot of tutorials on create.arduinuo.cc, but most of them have shown one 5V cable, one GND cable and one data cable, but mine seems a lot different:
It has 3 5V cables, 3 GND cables, DATA IN and a DATA OUT cable. How should I correctly connect this to my Arduino and use FastLED to assign colors to LED's?
Connect the grounds together (including the Arduino), connect the 5V to some appropriate power supply (around 16 Amps, not the Arduino), and the DIN pin to your Arduino output pin.
Unless you've got another panel, leave DOUT unconnected.
OK, that display is designed to be "chainable", so a number can be connected together for data.
You connect your 5 V heavy-duty power supply to the middle black and red wires.
You connect the "In" terminals to your Arduino. White to the Arduino ground, red to the Arduino "5V" terminal and green to the data pin you are using.
It is reasonably important that you actually power the Arduino via that three wire cable. A neat way of doing so if you are only using one display panel, is to de-solder the "Out" cable and use that to connect to the "In" cable connector. This is to avoid having current loops in the ground (or 5 V) wring or the possibility of having one part powered but not the other.