Howdy Wolfi - -
I live in Wyoming and have done six cross-country trips - plus, maybe, a dozen more throughout the West. I can't ride with you, but would be happy to give you any information you might need.
I am not sure when you are planning to do your trip; however, it should be after June 1. May is too early for the West, October is too late. Yes, 5 weeks is a short time, but you have some good options.
I do not know where you plan on starting. There is a beautiful trail from Washington, DC to Pittsburgh, Pennsylvania throught the Allegheny Mountains. It follows a historic canal then an old railroad. You could start from Mount Vernon - George Washington's home - ride by the monuments of Washington - visit Civil Wars battlefields - and Frank Lloyd Wright's famous Falling Water.
http://www.nps.gov/choh/http://www.atatrail.org/Then you could hop on Amtrak and go to Milwaukee, Wisconsin where there are beautiful rail trails through the countryside. I'm not sure where you are going in Minnesota - - Minneapolis-St. Paul? Then you could hop on the train again and head out to Montana and ride Going-to-the-Sun road thru Glacier Park - - truly one of the most beautiful rides in the world.
http://www.crazyguyonabike.com/doc/page/?o=lt&page_id=26439&v=156Remember that the United States has terrible train service - but the Greyhound bus is worse. In the two rides listed, they would be overnight but could be an hour or two late. Amtrak usually has only one train per day on long-distance routes. Checked baggage (Your bike) is limited to a few major stops.
Amtrak -
http://www.amtrak.com/servlet/ContentSer...2206&ssid=3My guess is that the Eastern and Midwestern sections would each take about a week - - so you would have three weeks for the West. Depending on your speed - you could ride all the way from Montana to Anacortes on Adventure Cycling's "Northern Tier" of if you want to ride the Pacific Coast in Oregon - take Amtrak again (and again overnight) from Spokane, Washington to Portland, Oregon.
e-mail me if you have questions.
Best - John E
Buffalo, WY