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

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

I substituted the power cords that came with my Merrill Audio Veritas monos with Shunyata Pythons and the noise floor,resolution,along with a more natural rendering of the music... did take a turn for the better. Great fit in my system!

5% gain is quite a bit to expect with any pwr cord change from just a stock thick gauge cord.
I’ve been using upgraded cords for a long time,generally make my own,and without question they do lwr the noise floor,have better defined dynamics,and are generally smoother and more refined across the board.

I’ve owned many class d amps and I found that with all of them,they like being powered up all the time.My latest amp a Lyngdorf 2170 definitely likes being left on,not on standby,all the time for the very best in sound and also is ready to go at any time.

I recommend that you try a reasonable priced cord and listen for yourself and compare to a stock cord.

Kenny.