I used to work in a large industrial electroplating plant, and we would regularly use something like 800 amps at around 4 V. That required some very odd-looking transformers and rectifiers, but it could be done.
Potlines that smelt aluminum from ore will often use currents in the order of 40,000 amps, again at some fairly low voltage. And, again, the rectifiers and transformers are quite spectacular to see, as are the busbars to connect them.
1000A at 5V would be 5KW, which is not a particularly unusual power level but handling 1000A is never straightforward. It requires conductors of significant cross-section aluminum pot line and bus bars.