In the D&D 5e Player’s Handbook, there is a variant option called Skills with Different Abilities:
Normally, your proficiency in a skill applies only to a specific kind of ability check. Proficiency in Athletics, for example, usually applies to Strength checks. In some situations, though, your proficiency might reasonably apply to a different kind of check. In such cases, the DM might ask for a check using an unusual combination of ability and skill, or you might ask your DM if you can apply a proficiency to a different check.
Essentially, the rules allow for a DM to ask for an ability check but the player can apply a skill, normally associated with a different ability, to the check.
For example, attempting to blend into a crowd by engaging in conversation and acting like you’re meant to be there might call for a Charisma (Stealth) check. So the player would roll a Charisma check and apply their Stealth proficiency – if they have one – to the check.
However, not everything is clear cut, there are often overlapping skills which could equally apply. To use the same example, one could argue that it is not a Charisma (Stealth) check, instead it is a Charisma (Deception) as you’re deceiving the people about your intentions or (Persuasion) as you’re persuading them you’re meant to be there.
Another example, a player wants to parkour their way up to the top of some buildings. One could equally argue that this a Strength (Athletics) check as that is the usual ability associated with climbing or that it is a Dexterity (Athletics) check as you have to be exceptionally precise to quickly grab small ledges so you don’t fall to the ground.
So, my question is, when a player describes an action they want to take, how do you adjudicate which skill and ability to combine to make the check?
Answers must be backed up with your experiences of using this variant rule