I need a little advice from you experienced gurus.
Currently I'm DMing a level 10 party of four PC's in a custom campaign setting, and the combat is going great. The players are engaged, having a blast, and routinely tell me that each session after the last becomes their new favorite.
The problem is, I'm having trouble making non-combat as interesting as combat.
That's always been an issue in D&D, and 5e is no different. 5e's base assumption is that players will describe what they want to do and you will rule success, failure, or roll vs DC. That's prettymuch it. If the players are already interested in a non-combat scene, and you're good at making successions of snap ruling like that, it works fine - it's barely different from just freestyle PRing the scene, but it works fine. It does nothing to generate interest, though, and the first step is /player describes what he wants to do/, which, in the absence of interest, is not going to happen.
Combat generates interest with a sense of jeopardy, and the excitement of an action scene. A non-combat scene can include action or jeopardy or excitement, too. But a broken axle or an interaction with a shopkeeper isn't that kind of non-combat scene. Even scenes that have that potential usually require player buy-in, up front. If you don't care who rules the kingdom and can't even remember the names of the plotters, a court intrigue scene is going to be boring.
So the primary thing is lay groundwork that makes the players care. Sad to say, most players care about the survival, power-accumulation and general aggrandizement of the their own characters and not much else. Combat figures directly into that. The PC's survival is on the line, he displays impressive abilities, and he at least gets experience points, if not an opportunity to lute a magic item (particularly important in 5e, as getting magic items makes you 'just better'). It's hard to roll all that - or even /any/ of that - into a non-combat scene.
Even assuming you could, combat has yet more stuff going for it. A lot of mechanics are brought up in combat. Action economy, hps, attacks & saving throws, damage, concentration, adv/dis, positioning, and, of course spells.
Out of combat, you're mostly making skill checks, which is like resolving a combat with nothing but attack rolls - no damage, no saves, no action economy, no tactics, nothing, just roll d20 vs DC. (Sure, those'd be some fast combats, but they'd be boring). Not only that, but in 5e combat you at least have a choice of possible attacks, you can be confident your longbow attack is going to be different from your longsword attack, and if your STR is higher than your DEX, that getting in close and using the sword will be an advantage. Out of combat, all you can do is describe an action that you /hope/ will get the DM to call for one of your better stats and a proficiency you have. So there's very little sense of player agency, as well. Of course, when a non-combat spell or ritual applies, casters get some agency.
So, what does that all mean? First of all, your skill-challenge-like mechanic is a good start. It gets everyone involved, gives them a teeny bit of agency in what skills they use, and means that everyone needs to contribute to success, so you have a teeny bit of jeopardy (in that a failure would presumably be bad). But, it's just a start. If you could find a way to add more depth to the resolution of skill checks, that'd be awesome - I've never thought of one, though. Failing that, you could still help things by providing a greater sense of jeopardy and of player buy-in to the challenge mattering. And, you can give rewards for success - exp, at minimum. But, something akin to the 'just-betterness' of magic items would be better. In an exploration challenge, treasure, including magic, is a possibility. In an interaction challenge, reputation, influence or privileges could result (or be lost). You'd have to give those things actual campaign and mechanical effects.
Privilege can be very important. For instance, if the premise of the campaign is that the PCs are all members of some order, and ongoing participation in the party's missions prettymuch requires maintaining that membership, then social challenges can carry a sense of jeopardy, as each offers a potential for disgrace and expulsion from the order (in essence, character death, since the PC can no longer participate in the campaign).
I guess I'm just hoping to hear some examples from posters on how they run the game outside of combats. How do you resolve scenes like chases, infiltrations, a political soiree where you're trying to coax out info, a trek in the wilderness trying to find an ancient ruin, etc. Do you use skill checks? How do you determine who gets to go, how many checks are involved? How do you determine DC's?
Really, any suggestions will help.
One thing that can help is getting a visual representation out there, and adding something to track and show progress or consequences of failure beyond just tallying successes (even if it /is/ just tallying successes, but visually). Think of it like creating a game within the game, with it's own rules and victory conditions. You can use randomization or player choice to make certain skill checks available instead of others, or at different DCs, or to put different rewards or consequences on the line. Take that soiree, for instance - players could choose to approach a potential source in a group conversation, at a meeting, in a private closed-door conference, or in quiet corner somewhere (or in the course of some other optional activity) - or, a player might 'mingle' or join a dance and just see if anyone lets something slip, so there's a random component, as well. Or, in the search for the ancient ruin, you might have a boardgame-like or flow-chart-like map set up, and successes or failures move you along it - closer to the goal, or into dangers, depending on where they land as a consequence of their choices and checks (and what choices & checks are available could depend on the current area, so, for instance, there might be a 'high ground' area that they can find fairly easily, that offers lower-DC perception checks to identify harder-to-find areas).