Not necessarily with the bulk oils. For retail oils, they will typically make the prices the same (as we see with GC -- obviously better quality base oils, but same price as the 5W/10W-30 Syntec). But with bulk oils, it is entirely conceivable that the 5W-20 would be more $$$ because they must use higher quality oils.
Furthermore, many quick lubes, even recently, were not stocking bulk 5W-20 as customer demand was/is weak. So the 5W-20 they might be selling would be out of gallon or quart containers, leading to the price discrepancy.