Voltage is pushed, current is not.
A device drawing 5v@5mA from a 5v 1000A supply will continue to draw 5mA if you increase the supply to 100V or 100,000A.
Or at least it will until it's fried from the extra wattage. 5V@5mA is 0.025W, but at 100V, that same 5mA pull is half a watt.
But it's always 5mA