Can a power cord increase the resolution of an Class D (SMPS) amp by more than 5% ?


5% in relation to a stock power cord.

I can’t really trust dealer comments. I am more interested in reports from audiophiles. 
Whats your story? Did you manage to increase speed and resolution of your amp ? (without losses in the bass area)
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It's impossible to answer the question because there's no way to quantify this mysterious 5%

I would submit that changing out the amp power cord while leaving in the stock power cables of all other components, will probably have little benefit.
 Nothing mysterious...

100% - 2 times more resolution, like a new component (unreal)
50% - outstanding upgrade
25% - really good upgrade
10% - good upgrade
5% -  noticeable improvement
under 5% - 100 AB Tests needed to find a difference.

I think so.

Prior to the Stereophile review I purchased my first switching amplifier a PS Audio HCA-2 to fill in for a solid state amplifier out for an upgrade. We had recently moved into an 1972 vintage California ranch home.

Right out of the box the PS Audio's presentation was somewhat forward with a startlingly plate glass transparency and a remarkable lack of congestion at higher listening levels. It wasn't long before I noticed I could hear what was being played faintly through a bedroom clock radio.

We began a major remodel which included upgrading the electrical service from 100 to 400 amp service. This required the utility to replace the cable from the grid. My electrician replaced the aluminum cable from the new main breaker to the new breaker panel and two sub breaker panels one of which was for audio only.

From the audio sub panel I used 10g for hot and common and an 8g ground within an uninterrupted metal clad BX housing to the metal receptacle boxes containing Hospital grade isolated ground receptacles and 10g DIY double shielded power cables. Bottom line here was beefy conductors and shielding for the area I'm in. Two runs to the Hi-Fi and two runs to the HT were just under 1K. Highly recomended.   

During all this the amplifier was steadily breaking in but that couldn't account for the degree of audible improvement we experienced nor could I attribute it to just the power cords.
The improvement was much more than replacing all the cheapo speaker cables and interconnects with my Cardas Golden Reference and slightly less than replacing my very old Shure V15 with the Benz Ruby Z.

One constant I've experienced with switching amplifiers up to my now dated Hypex nCore 400s is they all liked thick copper cabling and nothing silver or silver coated. NuForce speaker cable was noticeably better than the Cardas, if you can find it.