Just use whatever is the latest version available for react-native
- Create a new project
- Take all the libraries installed from the old projects package JSON
- Install them in the new Project
- Copy the SRC files for the project
- If there was any configuration file changes do those as well
- After doing all this run the project if there are issues stopping it
Debug them one by one.
Problems you will probably face
When you will install latest version of the libraries, sometimes a piece of code of configuration might have changed so you will have to look for those and change them accordingly.