Help Getting Chip Part Number, Logic-Driven DIP 12V/24V Power Control
It is called logic level translator, level shifter.
You can also use MOSFET low-side gate driver that usually input 2-5V and have their high side at 20+V.
For the down conversion, you can simply use a resistor divider.
EDIT
The question isn't very clear as to how much current you want to switch.
If you need to switch a load with a couple of amps based on your schematic, you can simply use a N Channel MOSFET, if you switch at low frequency you can directly drive it from 5V, just make sure the MOSFET Vth is lower than 4V to keep some margin. If the load is inductive, add a flyback diode.