Upvote:2
My friend recently did a 7 - 8 day hike from Tateyama to Kamikochi. It's quite intense, but you can either choose huts or just camp at sites or wherever else. You could easily cut parts out to fit your schedule.
This isn't my friend's blog, but it is the same trek with more info
If you're looking for more specific information, update the question and I'll relay answers back.
Upvote:3
Haven't been myself, but have always heard that the Shiretoko Peninsula at the northeastern edge of Hokkaido is the crowning jewel of natural Hokkaido. The mountains there are not as high, and you'll be out close to the sea facing Russia.
This guy lives in Hokkaido and has done a a big hike around Shiretoko.
Also, though it would not take your entire 5-7 days, I can confirm that Rebun Island makes for an amazing hike in August. It is an island located off the coast of Wakkanai, the northern-most edge of Hokkaido (and Japan).