For the Europeans on HN: on the East coast of the US, the furthest you can get by train in ~5h is roughly Boston to NYC, or NYC to Washington, DC. Both are roughly equidistant (~220 miles, ~354 kilometers).
One of the perverse things with our passenger rail network is that you can actually take take trains that "only" take 2.5 hours, but: they run nonstop point-to-point, and any subsequent connection you make (e.g. to Richmond, a major city in Virginia) will be on a diesel train that shares trackage with CSX or another major freight line. The end result is that traveling the extra ~90 miles from Washington, DC to Richmond generally takes over 3 hours, when it should really take less than an hour.
Boston to Philadelphia a closer approximation. The Acela is scheduled for 5h 1m for that trip. I travel between Boston and New York by train frequently, and even the slower regional service takes < 4 hours. Either way, still not a great comparison to Europe.
Sorry, this was confusing wording on my part -- I was trying to say that Boston/NY or NY/DC is consistently under 5 hours, and that just about everything else is over 5 hours, illustrating a gap in our network.
NYC to DC is also consistently around 3.5 hours, even with the slower NE Regional.
With a modern high-speed rail line, you'd theoretically be able to get from NYC to Chicago in around 4:15, even when accounting for stops along the way.
That's an average of 300 km/h. There are already lines in service elsewhere the world that are that fast.
The fastest service was Wuhan–Guangzhou, which averaged 313 km/h on non-stops, but is not run any more.
Chicago-NYC with stops would probably be 5 hours, which is barely competitive with flying. The intermediate stops would potentially make it viable though.
I would take a 5-hour train from NYC to Chicago over flying, because of the extra comfort and because getting to/from the airport on either end is a hassle.
However, modern high-speed rail lines are capable of 350 km/h top speeds, and there are lines that average 300 km/h, with stops included (e.g., Beijing-Nanjing).
5 hours, from New York Penn station to Chicago Union Station (as opposed to killing an hour to JFK/LGA/EWR and another hour from O'Hare), without having to be an hour early on top of that so the TSA can fondle you, sitting in a normal sized chair, allowed to stand up whenever you want, and complimentary wifi the whole time. Yeah, that's competitive with flying.
One of the perverse things with our passenger rail network is that you can actually take take trains that "only" take 2.5 hours, but: they run nonstop point-to-point, and any subsequent connection you make (e.g. to Richmond, a major city in Virginia) will be on a diesel train that shares trackage with CSX or another major freight line. The end result is that traveling the extra ~90 miles from Washington, DC to Richmond generally takes over 3 hours, when it should really take less than an hour.