There are a few variations on this dimension:
3/8 x 5/8 so that the frame sits 1/4" from the top edge of the box is "standard" -- or at least very common. This leaves the frame about 1/8" from the bottom of the box. I have all my boxes set up like this, as I started with Kelley boxes and they have this dimension.
Older boxes, especially deeps, tend to have a 3/8 x 7/8 deep recess, with a folded metal rail that holds the frame up about 1/4", making the recess 3/8 x 5/8" with space for bees to go under the ends of the frames. May or may not be what you want, and you must get the folded metal rests rather than flat metal ones or your frames will sit too deep.
Occasionally you will find boxes with the recess cut 1/8" deeper so the frames are flush with the bottom of the box. This is fine if all the boxes are the same, but you run into trouble if you mix them with the "normal" boxes with 3/ x 5/8" recesses. The box below will have too little bee space and the one above will have too much, inducing the bees to make burr comb or glue the frames in the two boxes together.
And I've also heard of people wanting a 3/8 x 3/8" recess so the frames are flush with the top of the box and all the bee space is below the bottom bar.
All of this will work if all the boxes are the same, but I'd stick with the 3/8 x 5/8" recess, or 3/8 x 7/8" with folded rest. You should be able to mix those with any standard manufacturer's boxes without problems.
Peter