In general, you want there to be a degree of proportion between the stitching and the project. Having a very thin project with very large stitches can (emphasis CAN, not saying it WILL) look out of place.
For 5 mm stitching I use 0.8mm thread (or, in Maine Thread, 0.030"). I agree that this stitch spacing is pretty large. I would minimally move to 4mm stitch spacing, at which point I would use 0.6mm thread and needles that were about a size 3, but could be 1 or 2. I use Osborne harness needles mostly because they are so available.
-Johnny Longpants