Normally, muting by using the palm to prevent sympathetic ringing (especially when using gain) is recommended, but then we see players like Batio who does no right hand muting.
I notice that the 5th and/or 6th strings aren’t muted when I’m playing the first strings, should I be concerned about this when using DWPS?
Just listen and see what happens. If it rings, you’ll have to do something.
If you can play without muting and its still clean that’s great. It’s a tonal option that not everybody has.
Anyways you should be able to mute, there are certain situations whrere it’s not your playing causing the strings to ring.
In the good old days of garage bands muting equaled surviving 
Muting for many is a two handed affair. I often might not even notice my mute points as they’ve become ingrained. The side of the hand, the inside of the joint between thumb and index finger, the side of a finger tip, etc… But that said, and others have basically said, if the string isn’t excited, no need to mute.
It’s an essential component of slide guitar, so there might be some knowledge to be gained from players that specialize?
Good luck.
Try this - play (and record it if possible) a lick/run that covers all strings -play it in the way you normally do. Then grab a sock and tie it loosely around the neck towards the headstock so that it mutes all strings and play/record the same lick. Listen back to them and see if there is much difference with regards to extraneous noise. If there is considerable noise (or enough to bother you) on the unmuted version, then you should attempt to explore muting options to employ. Don’t forget that there will often be strings sympathetically ringing out where no muting is used, but most cannot be heard in a band mix. Good luck with your quest!
Thanks for the ideas and suggestions everyone!