Temps can vary with these processors. Some will have a single CCD and some will have a dual CCD. The single CCD version runs warmer. I have a system with a 5800X used internally for benchmarking, we're using a Corsair H110i 280MM AIO and temperatures aren't an issue. I'd say 240+ AIO and you'll be fine.
Top end air coolers like the Noctua DH-15 will absolutely compete and probably beat 240MM AIO's. It's prohibitively tall for smaller cases. It's 165MM, so watch your cases available cooler height.
240mm or high-end air will do a great job.
I know someone with a 5800X and uses a NH-D15, it's quite amazing how well it performs for an air cooler.
Submit photos and a description of your PC to our build showcase
See other custom PC builds and get some ideas for what can be done
Services starting at $149.99