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Thanks for your information. I am new to this and that was my 1st question.
Kind of a test. I guess I took a lot for granite for assuming you should know that the 15' 2x8 sandwiched 1/2" in between is holding up ceiling joist and roof rafters and shingles (3 pitch 20' rafters. Shed type. I went from one wall to the other ( 3 1/2" each way in the wall). It is supported with a 4x4 on each side. Is this enough?
If header/girder/beam for roof and ceiling, then another factor comes in: snow load. Where are you located?
I don't actually understand the 5'-9" chart thing. Was that 5'-8" for 1 single 2x8?
The 5'-9" span is the distance from edge of bearing to edge of bearing, i.e., let's say you used 4x6 posts for the supporting columns, the maximum allowed distance between the 4x6 bearing columns would be 5 feet 9 inches.
That was for two 2x8 nailed together as one beam/girder, but not including any plywood.
The code addresses some basic factors, once the design becomes more involved than the basic factors covered by the code, then you would need to address span tables, species of tree, fb (f sub b or fiber bending of the species, and E modulus of elasticity, to important strength factors for lumber based on the species of tree), or have a structural engineer look everything up and run the numbers - the code is only prescriptive (do-it-like-this-and-this-will-work-this-way-under-these-conditions), once you are outside the information provided in the code, the code information no longer applies for design purposes, then it becomes engineering.
One way to look at the prescriptive measures of the code is to think in terms of one of the names given to a prescriptive code in the early 1990s - the Southern Building Code Congress International, in an attempt to allow builders to not have to use engineers for basic square and rectangular buildings was to name that standard, SSTD10, as "Deemed To Comply". If you constructed a structure falling with the size/height/length-width ratio/etc., and constructed the structure in accordance with that standard, the structure was "deemed to comply with the code" and met the minimum design requirements of the code, hence the name "Deemed To Comply".
While your question was short and easy, the answer is based on "It depends." and "it depends" on a lot of different information which needs to be considered before deciding if something is going to work. You probably do not want a post every 5-1/2 feet, which would mean you would need to increase the size of the beam/girder, (go to 2 2x12) or increase the number of components (use 4 2x8), or other variations.