LED driver high current and voltage
400 LEDs, with each LED taking 5v and 5A (25W each) is a lot of power, 400 x 25 = 10kW of power when they're on. With a 3% duty cycle, that's 300W average.

Your LED driver therefore needs some form of energy storage.

The maximum pulse duration determines how much storage you need. If you want 1uS on and 30uS off, you can do that with a few small caps. One second on and 30 off is a rather different, 10kJ takes up a lot of room. I suspect your target is somewhere between those two.

Next you have to consider efficiency. Is the energy expensive and must be husbanded (portable battery) or cheap (mains, or vehicle generator)? A current shunt, mosfet and opamp will result in an inefficient driver, you will need switch mode to improve the efficiency. Even if you're only 33% efficient, 600W is not too much heat to get rid of in your electronics if it means a much cheaper circuit implementation, or is it?

Add pulse timing and energy costs to your specifications, and clarify whether you do really mean 10kW of LEDs, and then this or other answers can guide you better where to go.