back in time by flying around the earth?

Answer

The answer to your question is actually already in the question: if it is HERE 3 AM on Tuesday, in the IN AMERICA (East Coast) it is still 10 PM on Monday. It is therefore not the case that you travel 5 hours back in time, because those two times that you compare apply at other locations. Even if you would start that journey here at 3am and complete it in 1 minute, you would not have traveled back in time, because when you arrive in the USA it will be 3h01m here, and that is later than the time you you left. To see whether two times later or earlier are opposite each other, you must of course calculate them according to the same time zone.

By the way, suppose you can indeed travel to the USA that fast, and you just fly around the whole world. Somewhere over the atlantic ocean the day will jump from Tuesday to Monday (yeah!!) but if you fly around the earth you will cross the international date line on the other side. That is an imaginary line through the Pacific Ocean, roughly at 180° west or east longitude where the date on the left (on the west side) is always 1 day later than the date on the right (on the east side). While you are flying over there, your date will suddenly change from Monday to Tuesday (bad luck!!). So going back in time, or even in the date is not possible.

So there are two date lines: one fixed in the pacific ocean that navigates between the islands, and a second that orbits the Earth every day and sweeps past us at midnight.