BTU is a measurement of heat/energy
Watt is a measurement of power (energy/time)
A BTU is similar to a joule, a BTU/hour is similar to a watt.
When an AC unit says 5000 BTU it means that the unit will remove 5000BTU/hour from a space, though this depends on the temperature difference. It is not a measurement of how much power the unit is drawing. That would depend on the specific unit you are looking at.
Yeah, note that it does this via a heat pump so it takes much less than 1400W to move the heat. I have a 10k BTU window a/c and it's about 400W (that's just for a/c, not for miner cooling).
Also since you know that 5000BTUs are displaced you know that it can cool 1400W of energy lost from the cards as heat. Assuming the 80% efficiency, 20% loss, that means you can cool 7000W of equipment for about 250W. In reality it's probably more because you don't have to seal the box.