I've created a draft that I hope will illustrate some of the things you can do. The first five treadles show what happens if you use the same pattern in blocks 1-5, 6-10, and 11-15: you get an allover pattern. So if you want to weave plain satin, or a 2/3 twill, or anything at all that's weavable on a 5-shaft straight draw pattern, you can do it.
The second five treadles show what happens if you use three different patterns for shafts 1-5, 6-10, and 11-15. Shafts 1-5 are tied up for satin, 6-10 are tied up for twill, 11-15 are tied up in a pattern I made up. If you repeat this treadling, you get satin on shafts 1-5, twill on 6-10, and my made-up pattern on 11-15.
The last ten treadles show how you can alternate blocks to create a checkerboard pattern rather than stripes. Treadles 11-15 and 16-20 are reverses of each other (what was up is down, what was down is up). By alternating them you can get a checkerboard pattern.
You don't have to use inverses for creating alternating blocks. You can alternate any treadling you like, e.g. you could alternate treadles 1-5, then 16-20, then 6-10, etc. You'd get a mishmash pattern but it would work.
PM me if this is confusing!