As to the needle size, #5 is way too small for a worsted weight yarn. I used to make convertible mittens this way a few years ago. The pattern called for it and I didn't know any better because I was still a novice knitter. You can do it, but not without a lot of cranking to actually knit the stitches and a few curse words thrown in. I now knit these on a #8 and have modified the pattern to suit me. If you're getting 6-8 stitches per inch, this is more along the lines of a #1 to a #3 needle. Six stitches per inch is about what my LYS recommended for knitting socks on a #3 needle with thinner sock or fingering yarn. This would be about a #1 or #2 in the weight classification on the label.
Edit: Reminds me, I need to finish the convertible mittens I'm doing. The ones I made several years ago have worn out and my son asked me to knit another pair for his girlfriend.
Welsh corgis are cool.