What are your computing requirements: gaming, video editing, bit-mining, school work.....?
"Cheap" is subjective. What is your budget?
You are also likely limited/constrained regarding motherboard choices by the components that you have already have.
Motherboard spec's list the supported components. So your immediate need is a motherboard that supports the Ryzen 5 5600x and the RTX 3070.
And you must indeed visit the websites for all components for updated information regarding support and installation.
Motherboard's manufacturer's provide an QVL (Qualified Vendor's List) that usually requires close attention to details. Both what is said and what is not said.
Start here:
https://www.tomshardware.com/reviews/best-motherboards,3984.html
Often overlooked: case, cooling requirements/space, PSU.