You would need a single pole 3 position switch. I know of no switch of that type that is capable of handling 15 A.
The switch arrangement would be like this - if you should find a suitable switch:
When you don't find a suitable switch, relays can be used to do the heavy switching with a 3 pole switch to select the relay:

Here the switch is connected to the 5 V supply only. All relays have 5 V coils. If you use 12 V relays, connect the switch to 12 V.
By moving the switch into one of its three positions, either relay coil 1, coil 2 or coil 3 are activated. The respective relay contact is closed (shown above for 12 V), all others are open (3.3 V, 5 V). The output is supplied by the selected voltage.
Of course the relays used need to be able to support 15 A on the contact side. Automotive relays will possibly be good candidates as in a car high currents are often switched. The relay coil is then a 12 V coil (typically) and the 3 position switch needs to be connected to 12 V , too.