First thank you for these comprehensive responses, they are so far more than I expected.
I will respond first to the questions that 5ekyu posed as they are more in depth than I had even really thought of myself, and I think they cover what everyone else has asked. My general dislike for the 5e system stems from my feeling that it is too limited in scope, that the skills are so broad that I'm often being left with uncertainty about how to apply them. Also, I have found that more comprehensive systems give players ideas on how to use skills themselves they may not have thought of.
Can you name two things that the 5e skills system *currently does* that you like and want to keep?
I do like that the current system is simple, and it meshes well with the manner in which D&D is played in that it uses a D20 and is tied to both the proficency bonus and the attribute bonus. I like this and would like to keep it.
Can you name two things that the 5e skills system *currently does* that you dont like and want to scrap?
As I said above, I'd like a system that offers more skills. I really love the Shadowrun system and how skills work there, which is entirely inappropriate for D&D I understand, however the depth and scope of the skills offered lends itself to suggesting to players how to use them, and helps to define characters.
Can you name two things that the 5e skills system *currently does not do* that you like and want to add to it?
I'm certain that the current system can accommodate all that I would like a more robust system to handle, however as stated a couple of times now, I do not like how general it is.
Can you name two things that the 5e skills *currently does not do* that you don't like and want to make sure doesn't get added by your new changes?
My group is filled with new players. Though they have been gaming together now for nearly two years, they have only gamed together with very little variation in the player base. I'd like to expose them to a broader skills system that would lead them to think of using skills in new ways. I think the 5e system would allow them to do most anything they can think of currently, but I wish for them to see new role-playing opportunities that a more robust skill system would suggest to them.
Thank you for your time.
Ok so what i am hearing here is that you want more details on specific skill uses - set examples and DCs - both to serve as a guide for the Gm and a nudge for the players. Your hope is that it will drive players to use them more or in different ways and that it will give you a perhaps more consistent framework on how to apply them.
if that is way way off, not what you were putting forth, then i apologize.
So, let me give you my advice based on similar goals but different outlook.
Go the other way - go left instead of right but wind up at the same spot.
MY EXPERIENCE - says that the longer, more detailed laundry list of pre-fabbed noun-verb-dc-result "events" a system gives the less imaginative it leads players and GMs to be. if your system has a list of 30 uses for athletics with modifiers and DCs for all sorts of different thing, the actual play tends to be "fit my actions and choices into this list somehow." if the system says "here are a few skills and ability scores and a mechanic" you get a lot more variety in actual play choices made.
So, based on my experience (in multiple systems and skills etc) and my own current games in 5e, the route i would suggest to try is the following.
Consistent DCs: As Gm come up with your own simple, easy to express "here is what DC means in my games" and stick to it. For things like saves and such, the rules are fine. but for traps and locks and walls and keeping balance, have a common reference that you can express in a hot minute for any scene. Then apply it with lots of obvious descritions that show them what it is. The DMG section on setting skill checks is fantastic for this.
IN MY GAMES: i use the DMG 10-15-20 is it (except for special circumstances.) I think of it as "who set this up and how good were they" or "who could look at this and say "hold my beer" and how good are they"?
DC 10 is easy and it is for cases where neither skill (proficiency) nor aptitude (primary ability and focus) are required. So, an innkeeper doesn't really care about security on the rooms has DC 10 "locks" on all the resident rooms, except for his own - more on that under special." That wall around the village put up by farmers etc might be only DC 10 to climb if they had no soldiers experienced at fortifications
DC 15 is for the "guy" has either skill (proficiency) or aptitude (primary ability or focus.) So an innkeeper who used to be a burglar but long since retired might be Dc 15 locks guy. That village wall might be DC 15 if there is a retired soldier or carpenter or mason.
DC 20 is for "masters", the guy is an expert with both skill (proficiency) and aptitude (primary focus and ability.) You can figure this one out from the above.
SPECIAL: this gets into a +5 or -5 (advanatage or disadvantage) for how much effort or time or resource went into it above the norm. A rich shopkeeper willing to spend a lot more money on security or a village where their is someone with wealth or extra manpower backing the wall - +5 (advantage for help - if you will) to whatever the DC would be. The reverse for someone who skimps and cuts corners or really does not really care - or for some cases where they had to rush the finish and its not really a fully complete thing yet.
Extra time/resources +5
Insufficient time or resources -5
This produces 5 - 25 range across the campaign - same at 10th as at 15th as at 1st. My PCs met a DC 20 and a DC 25 check in their first session at level 2 and just met a DC 10 one recently. be consistent and show them descriptively how they can see the "DC" in the setting.
Then if they walk up to some mud village with a fancy wall or some dive with a very well-built security system, they can go "what is up with that?"
Auto-success - i use the DC10 easy is automatic for proficienct checks unless you have advantage rule from the DMG.
I generally disregard the other DCs for non-character trait tasks. i find 5e is rather inconsistent in their DCs in modules and such and *really* what matters is the DC you set.
I would recommend you look at the DMG skill proficiency options for *less skills* - specifically for background based skills, where what is required is for the PC to tie "what he is doing" to his background and training, not to a skill list. That moves the "what i do" more into the dramatic than the "checklist". This syncs well with a descriptive-based Dc as i describe above.
So, my suggestion is to try to spark the imagination with "less rules specifics and definition" before you go to more defined lists.
My group has played tons of systems at all sorts of degrees of crunch from 1e dnd to black book Traveller to HERO to shadowrun to Cyberpunk 2020 to Amber to vampire to T20 to traveller with Striker to RollMaster etc etc etc. We never found "more crunch" or "more lists" to spur more imagination. They did shape the events, but in doing so they also limited our in-play perspectives and outlooks.
Also, for most skill use i always point to the Ability Check definition in the PHB where any failure can be a "some progress with setback" - not just pass/fail. that is an awfully potent tool in the Gm to bring skills to life in the campaign.
"I go hunting and scavenging."
"Make Wisdom (survivial) foraging check. The area you know is sparse but not barren - so wont be that hard but not easy enough for sure success." Code word for DC 15
"Rolled net 11. Dang it"
"Ok so you found some smaller game and bagged some stuff. Get 3 lbs (Wisdom modifer) and roll a Perception check."
"What?"
other players "You just went from the hunter to the hunted - cuz some beastie just made *its* hunting check and found you! HAHAH!!"
Everyone grabs dice in anticipation of the *possible* conflict depending on how our scavenger handled himself.
Final bit - Definitely use the Swapping ability scores bit from the PHB - Strength (Intimidation) is an obvious case for brute force coercion. Con (Performance) perhaps for more subtle ways of influence that may take all night (in-game time not in game-play time unless that is your thing!)
***
That said, this is how i would recommend trying to achieve the goals you set forth, but it is the opposite direction you had originally leaned. if thats because you have tried lighter more self-managed-consistent approaches and found them lacking then hey, thats fine. But in my experience, no longer list is gonna be the right fit that hits the imagination dial to 11 and also gives you the room to maneuver as freely and consistently. thats because a list tells you to check the list for how tough the wall is... while the approach i outline above is for *you* the Gm to decide *how tough the wall is* based on your chgsen setting and reasons and then tie the description and DC together to match that.
DC IMX is better when the first question is WHY and the rest follows from that.
Hope this helps even tho it is not the direction you were leaning.