It's called non-mechanical freeform roleplaying, backed up if needs must by at most one or two existing skills (e.g. Perception), and it can be done every bit as well in 5e as it can in any other RPG.
For "non-mechanical freeform roleplaying" you do not need D&D.
So if you want to do non combat campaigns you would be better of with a system which offers more than one or two existing skills or don't use a system at all.