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5 days is basically the bare minimum amount of time you need to make this trip safely (guessing you're going from around Manchester to Seattle?). Having said that, that does not allow any extra time for major detours, so Yellowstone is pretty much out of the question unless you take more time.

In fact, doing this as a camping trip is going to be pretty difficult as it is to cover that much ground that quickly, because camping by its nature takes more time. You have to factor time to set up and tear down each day, and campgrounds are usually not right off the freeway - especially not National Parks and National Forests.

Having said that, I wouldn't limit your camping options to National Parks and Forests either. There simply won't be many of them on your route until you get well out west, and they are often going to be harder to get to. There are a lot more camping options, however. State Parks are a great resource, and will be much more plentiful. There are also often be county, city, or other camping options run by local governments you can take advantage of for cheap camping. Paper Maps and atlases are a great place to see these options, because they will be marked right on the map with a triangle.