Snap-On made 5/16" drive ratchets and sockets a long time ago. And Blackhawk had a 7/16" drive back in the day. They dropped these and went with the standard 1/4" and 3/8" respectively. There were probably other companies making these but these are the ones I know off the top of my head.
What I find odd is in 40 years of buying, using and collecting old tools thease are the only 5/16 drive tools I have ever seen. The most common odd drive size I have come across is tools in 9/32 drive. Plomb and Snap-On being the most common found in this size. Thank you for your answers.