5/16 is halfway between too small & too big!
I would treat that as a minimum - 3/8 will not cause problems, and as I said if you have a long run it's not a bad idea to go up a size anyway to reduce flow friction.
If your chandler only stocks 3/8 or 10mm or whatever, don't worry about it. Just make sure your hose & barbs are in the same size series......