Is there a cheap relay that can control voltage from stuff like bulb lights with a 5 V control output?
You can use a 5V Solid-State Relay module to control light bulbs. They cost $4-6 from US-based suppliers and $1-3 from a Chinese supplier. Just hook up the supply to the center pin and the load to either the NO or NC pin. Supply 5V to the module and wire a digital pin to the module to control it.