Total current drop when using leds in parallel
It is hard to figure out just what you're doing. Is it possible that your LEDs have built-in current limiting resistors, and are intended for 12 volt operation? That would explain why connecting one to 12 volts doesn't kill the LED. Plus, if the LED takes 5 watts, that would leave 5 watts to be dissipated in the resistor, which seems about right. However, this would make the LED get very (very!) hot, and it's hard to see how this could happen. But let's say that this is the case. Then, when 20 LEDs are connected in parallel, the total current draw is 20 x 0.8, or 16 amps, and this would cause your power supply to limit. Are you sure this isn't happening? When you get 4.12 amps, what is the power supply output voltage?