Connecting parallel DC loads
Yes, you should connect red wires to +V in all cases and black wires to GND (or COM in this case, short for COMMON). Inside the power supply, the three COM terminals are connected together, and the three +V terminals are connected together.

Connect the Earth terminal to your mains earth (green/yellow or green wire).

Be sure that your power supply is rated for 12V and at least N times 5A output. Better to have more output current capacity, so that it's not running at full load all the time. Make sure your wires make good contact with the terminals, and the wires are thick enough to carry the current.