Upgrading Rails 3.2 to Rails 5

I have a Rails 3.2 project that has 30 models and about 20 controllers. It's not a super huge codebase and its pretty much an idiomatic Rails site.

Is there any advantage to just doing rails new and controller by controller, model by model, gem by gem just copy and pasting things in and getting everything running on a fresh Rails 5 instance?

I just see some pain trying to do an upgrade version by version. Is this a viable way to upgrade a project where I have written all the code and know the project well?