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

No.  Will it sound different?  Likely.  Will it sound better? Possibly.

As much as I dislike the crazy expensive over the top cables, replacing the stock cord with a $30 OFC cable (BLE Design on ebay) will bring an improvement.

Never improved the speed. It did lower the noise floor allowing more detail and resolution to pass thru. Stock cord supplied by Theta replaced with Transparent Reference PC. 

I've heard some owners of the Shunyata Research Alpha NR power cord that run class D amps say that it did lower the noise floor allowing more detail and resolution to pass through.
Personally, I have not tried it yet but perhaps in the future.
Seems like a large amount of money must be spent for a small margin of improvement, and it always seems to be that way with high end audio.

An Ansuz D-TC power cord did just what lak mentioned above with my Aavik U300. Because of that I can play almost twice as loud. I never would have believed it if I didn't hear it in my home. Not sure what percentage of improvement I got but would say it was lot. If I have to guess I would say 20 - 30%.
Yes it's crazy expensive too. Full List is 20K for 2M