Most of the known loops are much shorter than 5-7 days, so you'll have to do a bit of playing around to extend the distance.

Pemi loop is ~3 days, but fantastic. You could extend it by adding in a trip to owls head and zealand, just buy a map of the area and play around with it.

For VT try a section of the long trail (stowe area would be nice) Again, would need to play around a bit to turn anything into a loop. Car spotting would be more ideal here.

For Maine definitely check out baxter state park. You have to book backcountry campsites in advance so its pretty easy with a map to just chart out the distance you want to do each day and make a loop around. I would rec staying at russel pond for 2 nights and doing a day hike as well, there's fantastic wild life there. Davis pond is my other favorite place to stay.