What is the hardware/device that can switch a 5V and 12V (simultaneously) PC power supply lines?
This 5 volt DPDT relay would work for your project

What a relay is and how to understand the part I linked to you



The abbreviations stand for

SPST – Single Pole Single Throw
SPDT – Single Pole Double Throw
DPST – Double Pole Single Throw
DPDT – Double Pole Double Throw