Clean DC power supply from a dirty souce
If you need clean 5V, you could start with, say, 9V from a switch-mode supply and then drop it down to 5V with a linear regulator. A good old 7805 three-terminal regulator (with capacitors) might help.

But first, do make sure that the noise really is coming from the supply. Use batteries, or a lab-type bench PSU, as a temporary substitute for the switch-mode.