How does Power over Ethernet combine cores to send power over longer distances
POE typically uses 48V so 20W would be less than 0.5A shared over multiple 24 AWG wires.
For your 5V system, 20W draws 4A which is why you get too much drop in the cable.

Now consider your 24AWG wire. It has a resistance per meter you can find from many sources, here's one.
Given that from this chart a single wire has approximately 0.0842 Ohms/meter, that is roughly 0.25 Ohms for 10 ft. But you have to consider the loop resistance, so your wire R value is 0.5 Ohm.
Assuming you could pass 4 A through this loop you would drop 4 * 0.5 = 2 V in doing so.