A power mosfet can switch that load quickly and with very little loss. An IRF540N (only used that as an example b/c the part is easy to get) has an on resistance of 0.044 ohms and can handle something like 30A and 90V or so. You would lose around 2W of power in the mosfet and have about a 0.3V drop across it using your specs. But this is the most straightforward way to build a fast high current switch. If that loss is too much, you can parallel them to get a lower on resistance or buy one with a lower on resistance. You would need a simple interface circuit to connect your 5V trigger to the gate of the mosfet.