There's a few things that might help your search. My apologies if you know them already.
If you want exposure to the elements, then you either want stainless or galvanized. There are other chemical processes and coatings that will protect it, but those are the easiest to find.
If you've been looking for 5/16" ID tubing, it probably isn't going to give all the results you want. You are actually looking for pipe, not tubing. Tubing is measured by the outer diameter, pipe is measured by the inner diameter. A 1" tube should fit inside a 1" pipe. You can look for tubing, but you should look for 3/8" tubing with a .032" wall, that would give you an inner diameter of 5/16" (the wall thickness is half the distance, since the inner diameter is reduced by the wall thickness on opposing sides). However tubing has two major varieties, ERW and DOM. ERW stands for Electric Resistance Welded, they take a flat sheet, roll it over and weld the seam, so there will be a weld bead on the inside of the tube which will intrude into the inner diameter. DOM stands for Drawn Over Mandrel, after the tube is made they draw a die through it which removes the weld bead, making a smooth inner wall.
So you either need to look for 5/16" stainless or galvanized pipe, or 3/8" x .030" wall DOM stainless or galvanized tube.
Good luck.