Scott Christian
Hero
5e leaves it to the DM. You can use a wisdom climbing roll for example, if you wanted to combine the visual with the dexterity.This gives rise to the question: to what extent can a player augment their Climb Walls check (however that is handled in a given system - in 5e it is most likely STR (Athletics) ) via a Perception, Survival, Slippery-Walls-wise or similar check?
Some systems make this very straightforward (eg Burning Wheel; HeroQuest revised; 4e D&D, provided the context is a skill challenge). Some have no provision for it at all (eg AD&D). Some have a half-baked approach (eg Rolemaster; 4e D&D outside a skill challenge context).
I'm not sure what the canonical 5e D&D approach is to this.