This socket set was included as a gift in an e-bay purchase.  I thought it was 9/32" drive, but the extension and sliding bar both fit into a 5/16" square socket.  I'm not aware of 5/16" drive.  The set includes a double male extension, a sliding bar with slide containing both a male and female and 5 sockets one of which is 15/32".  The box is painted OD.  No markings anywhere.

Not that it means anything in this instance but Stevens Walden are the only ones I can think of at the moment that made a box hinged on the short side similar to yours but that where the similarities seem to end.
Any chance of seeing the socket profile. It may help with id.

bill

Here is a sample of the sockets.  In the first picture, the socket on the extreme right is the socket from my collection that the drive fits, it is 15/16"  Just as I have never seen a 15/16" drive, I have never seen a sliding bar with male and female on opposite sides.  Always a first time.

I haven't seen that odd drive size but the sockets look like early Indestro. The second set is Wards Riverside made by Duro/Indestro. The box is hinged on the end.
-Don

Bud Bolt's tool museum at Oroville, CA ( https://www.boltsantiquetools.com/ ).   has a display board with a whole range of drive sizes & most of them have at least one maker identified.  I don't find a direct link to it on the top level of the site.  Time to go to church & after that 8 hrs of work time,

I was recently on Alloy Artifacts looking at Hinsdale and they made a 5/16" socket set that was not marked, but it is not a match.

I'm pretty sure that the sliding T-bar is a Waldon, and those sockets Might be early Husky. Both were also makers of 5/16 drive tools.

I saw this picture of an early Indestro 1/2" drive sliding Tee on Alloy Artifacts and these are my unmarked 1/4" drive Indestro made sockets. I'm sticking with the 5/16" drive sockets being made by them.
-Don

I see the resemblance now Don. Indestro it is.

I also now agree, although I have three old Indestro set and none match.  The sockets in this set do match the Indestro  shown by Don.