For culvert size, go look at size used on the county roads on either side of this place. Nobody can complain if you use the same size or bigger than the county or state around you. They should have engineered their culverts to the proper standards anyway. Since your area may add some drainage, I would pay particular attention to the size of any downstream culverts but don't go smaller than what they are using on either side.
You are probably looking at a squashed/oval style culvert.
Not sure what is 5' to 7' wide, but your drive way needs to be at least 12' to 16'. Your vehicles and tractors are going to be 6' to 8' wide. Any truck bringing in building supplies will be at least 8 1/2' wide. Then you want at least a couple feet on each side for clearance and to avoid slip sliding around in the mud and driving off the edge. I'm changing my 12' pasture gates to 16' foot because of in the mud and stuff I have to slow way down to make sure I clear everything. Figure a single lane on a street or highway is 12 1/2' to 15'. Your culvert also has to be longer than your driving area is wide cause you can't pack dirt all the way out to the edge of a culvert for driving on.
My 2 cents anyway. Good luck. I have to put a couple in my self. One across a waterway for tractor access and then fix the dam of a pond. The city replaced a bunch of 6' storm sewer. A guy bought the old stuff and is selling them for $50 a joint which are about 6' to 8' long.
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Today's Featured Article - Tractor Profile: Allis-Chalmers WD45 (Gas Version) - by Staff. Beginning production in 1953, the WD45 had the same general look as the WD tractor which was produced earlier - but was much more powerful. This was due to the new 4-cylinder "Power Crater" gasoline engine with a 4 x 4-1/2 inch bore and stroke. Some people feel this was one of the most significant tractors offered by Allis-Chalmers in those days. Nothing in its weight or power class could match its performance. In 1954 they began offering the WD45 with the new "Snap-Coupler&quo
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