I have the LS10 and original case, but for the LS-P5, I think I would look at eyeglass/sunglass pouches/cases, plus perhaps a Pelican Micro if you have tough conditions. Companies like Case Logic sell many such pouches for computer and camera accessories.
I seem to have a good collection of pouches and cases from things like microphones and reading glasses, they are very handy for all sorts of recording items.