Yes, you can stay out for 5 days (you would sleep in your truck 4 nights on a 5/2).
The distance depends on the DC. For the Buckeye, AZ DC, we can run to Silver City NM (when we have that account), Gallup NM, Las Vegas, NV, and pretty much anywhere in CA, south of Porterville.
You get paid $42 a night to sleep in your truck, so it really isn't a big deal. Some of the drivers with more seniority can get shifts that allow them to go home every night if they choose. I couldn't do that since I live 120 miles from the DC.