What do the tubes that don't hold air look like?

If they have holes on the inside circumference, you have a rim tape problem. The rim tape has to cover every tiny crescent of spoke hole or you'll keep cutting tubes in that area.

If they have holes on the outside circumference, you are getting punctures. 5 punctures in 2 weeks is a lot. If you make a hapit of always lining up the tire label with the valve stem you can see if the punctures are all in the same spot (my bet). If that's the case, you have a torn or a piece of glass or something in your tire that you haven't been able to find and remove. Find it and remove it or buy a new tire.

If your tubes seem to have 2 parallel slits, you are pinching the tube between the tire bead and rim. It's an easy mistake to make.

There's also a "star" shaped hole but that sounds like a gunshot when it happens so I doubt that's you.

Incidentally, I used to save my punctured inner tubes and patch a batch all at once. It really doesn't take much more time to patch 5 than it does to patch just 1.