What is the best way to get to Narita airport from Shinjuku (Hotel Sunroute Plaza) at 5am?

Question:

I have an early morning flight! Do the bullet trains run early? Or is there an airport limo bus I can take? Trying to avoid taxis if possible!

Answer:

There is a Narita Express train which leaves Shinjuku at 5:55am and arrives at Narita at 7:15am.

It's difficult to arrive at Narita at 5am if you mean that.