This could be problematic. The clearances for a crank with standard diameter journals as delivered by Ford are as follows;
Connecting Rods; ............................. Low side clearance — 0.0011" (Ford Spec) ............................. High side clearance — 0.0023" (Ford Spec) ..............................Your Clearance — 0.0024"
Mains; ............................. Low side clearance — 0.0005" (Ford Spec) ............................. High side clearance — 0.0025" (Ford Spec) ..............................Your Clearance — 0.0039"
In general, mains on Aluminum blocks favor the low side of a spec when cold because the alloy blocks grow more than iron blocks when they come up to operating temperature. Cast iron has a lower coefficient of thermal expansion (CTE), grows less when heated, and therefore does not need to be as close a fit as an Aluminum block.
While at the upper end of the oil clearance spec, your connecting rods should not be a problem with a 0.0024" oil clearance. The 0.0039" oil clearance on your mains, however, is a problem. Is it enough to drop your oil pressure to 5 psi warm at idle? I can't say with any certainty but I don't think so. That said, it should still be corrected because it is enough to create unnecessary wear on the crank bearings. Your crank oil clearance is 0.0015" above Ford's high spec for the engine. If the block is aluminum, the clearance will be even greater when it comes up to temperature. I would consider this a show stopper.
The pregnant question is why your engine builder did not correct this. There are two common ways to get this much clearance. The first involves someone polishing down the crank journals to get the additional clearance. That is a lot of work. If this happened and you just reassemble the block with a fresh set of Mahle or King bearings your result will be the same. The other possibility is an align honing job that went bad and left the bores too big, releasing crush on the bearing and allowing the increase in oil clearance.
If the additional clearance is a result of a bad align honing operation the mains have a much-increased possibility of spinning in the block (because of reduced bearing crush). This will damage both the block and the crank. If your main clearance really is 0.0039" this is something that needs to be corrected. If the problem was an align honing job gone bad, the block needs to be fixed.
Of course, it is also possible that someone erred in their math calculations or oil clearance measurement or ??. If that is the case, your oil clearance may still be within the Ford spec. However, if the crank was polished down unless you can find an undersized main set, you are in the market for a new crank or a repair of your existing crank. I would go the new crank route.
The 800 lb gorilla in the room is the how did this happen question. You need to determine the answer to how the clearance got to that over spec number — it was not done at Ford.
While I am not saying it is not the reason for your low oil pressure, I am still suspicious. The oil pump you are using is essentially the high volume (comparatively) 3V pump that expects to see VCT hardware on the nose of the cams, powered by engine oil pressure and operated by the onboard ECU. The VCT hardware is notorious for using a lot of oil. IMO it is more oil than would escape from a 0.0015" oversize oil clearance applied to the mains — but, I could be wrong. The only way you will know with certainty is to replace the mains with a set that provides OEM spec clearances.
When you do the rebuild be sure to, in the immortal words of Captain Renault in the movie Casablanca, 'round up all the usual suspects' and check everywhere for potential oil leaks.
My bet on the excessive main clearance (if it is) would be an align honing job that was done incorrectly reducing the crush on the main bearings aggravated by an aggressive polishing of the crank journals — assuming the real oil clearance actually is 0.0039".
When the engine comes out for service you should use Plastigauge to measure the actual oil clearance on the mains before doing anything. Same thing for the rods. Whenever you are repeatedly measuring something like journal diameters, main bores, or connecting rod big end bores you can skew the readings by the amount of body heat the micrometer absorbs from your hands. Plastiguage eliminates this potential miscue and provides a very accurate oil clearance measurement. It will give you confidence in your investigative results and the corrective actions you should take going forward.