How long would it take to go from boulder city Nevada to Burlington Vermont on a bike at about 5mph?

You know the distance, you have given a speed, you can easily figure out how many hours of riding it would take. If you have a good touring bike, you could probably average a bit faster. It is not out of the question for a good cyclist to do 80-100 miles per day, but you migh want to take a day off from time to time. Figure on somewhere between 3 and 4 weeks