Circuit design to vary voltage and switch outputs
First way to do this that comes to mind would probably be:

(1) Find a reasonable AC to DC converter with Vout

(2) Find 5 DC-DC converters capable of stepping Vout to 0-15V based upon sensed resistor value

(3) Each of the above 5 DC-DC converters should have enable pins (most do) this will allow you to turn them on and off... along with control via resistor sense mechanism

(2) Find suitable microcontroller (MCU), with Analog to digital converter (ADC) and some variety of com protocols (SPI, I2C, UART....)

(7)connect voltage controlled resistor to sense of each DC-DC converter

(5) Hook the MCU up to each of the enable pins (one of the MCU pins to each)

(6) Purchase capacitive (or resistive) touch LCD screen with com interface compatible with MCU

(7) Program MCU/LCD combo to have touch screen buttons that let you select which DC-DC converter to enable

(8) Program MCU/LCD combo to have voltage selection slider and to display current output voltage 

(9) Have MCU ADC output votlage level necessary to all voltage controlled variable resistors to produce selected voltage.