How do I use multiple loops with a custom taxonomy?

I have created a hierarchical custom taxonomy called "verticals" that has three terms, 'news' 'stories' and 'essays'. On my homepage, I would like to have have three buckets that each lists five posts from one of the terms. Step one is, how would I go about that?

Step two, I would then like another loop below the buckets that lists another 10 posts from no specific taxonomy term, but does not duplicated any of the posts above.

I know it's a tall order. Any help?