I don't know how you came up with needing 5 V, but it sounds like a bad idea. You have a big efficiency problem, so spending a bit more on power electronics will make things easier and cheaper in the long run.
First, I would not bus around power as low as 5 V because that will require too much current. Having a roughly 48 V bus sounds like a much better idea. Each panel can then locally convert that to the specific voltages needed to run the LEDs and the electronics. That also gets around the problem of the bus voltage drooping from the power supply to the panels and between panels. The buck supplies on each panel can tolerate significant variations in the "48 V" power bus. And, because of the lower current there will be less variation in the first place.
Look at what voltages the LEDs need. Red and green will be near 2 V, but blue over 3. Red and green are probably close enough so that you can use one power voltage for both of them. Green has the higher voltage, usually about 2.1 V, so make a little more than that. You want it only high enough so that you can put enough of a resistor there to have the current be reasonably predictable despite variation in the LEDs. Maybe 2.5 V is a reasonable tradeoff. Red LEDs usually drop a bit under 2 V, so the regulation for red will be slightly better. Either way, this is still way better than 5 V. For the same LED brightness, just switching to 2.5 V instead of 5 V will save half the power.
Blue usually requires significantly more voltage, like over 3 V. Make a separate supply for blue. It should be a few 100 mV above the LED voltage, just like for the red and green LEDs.
48 V is a common voltage for off the shelf power supplies, and is the limit you are usually allowed before you get into legal regulations. There are various buck converter chips out there, or if you're clever you can maybe have a existing micro handle the buck conversions. Either way, these are readily available blocks you can use in your circuit.
It depends greatly on the exact power supply model, but in general I would not use it unless you example the schematics of your PSU.
Example 1: http://www.smpspowersupply.com/ATX_power_supply_schematic.pdf
In this schematics, +12V and -12V actually come from the same winding on the transformer.
The only difference is -12V has PR1507 diode rated 1.5A, while +12V has U20C20 high speed, dual diode rated 20 amperes.
So if your PSU looks like this, you can get +24V as long as you make sure the diodes do not overheat (it is quite possible that -12V diode has no proper heatsink, and thus it cannot handle full 1.5A for extended periods of time)
Example 2: http://www.smpspowersupply.com/atx-power-supply.html
In this schematics, -12V comes from a separate transformer using 7912 regulator. If you try to draw too much current, either L4 will not be able to provide it, so the voltage will sag, or 7912 will overheat. D5 will then start conduting and your -12V line will measure around +0.7 volts. If your PSU looks like this, you should not try to get +24V from it.
Best Answer
Passing 1000V at 10A through a diode does not generate 10kW of power. The power dissipated by the diode would be the forward voltage drop times the current. Only the voltage dropped by the diode counts toward power dissipated.