If you have murderhobos at your table, it might not be your fault.
Consider: One of the main motivations for both players and their characters is gaining XP and leveling up.
How do you gain XP in 5e?
Killing things.1 There’s a built-in motivation for slaughtering everything in sight in 5e. Of course, while you can (and should!) manage this with in-game consequences to murdering everyone or with out-of-character conversation around the table, we can’t quite get all the way around the fact that the game - purely mechanically speaking - does reward it.
I’ve been digging a little into some OSR stuff lately, and, while there are oodles of differences, one huge one from a game design standpoint is the idea of 1 gold = 1 XP.
It makes the mechanics of the game primarily about retrieving and returning with treasure, not murdering everything along the way.
I gave it a shot recently with this awesome OSR conversion of Dungeon of the Mad Mage a while back, and, while we didn't finish the campaign (I'd make some changes in retrospect), I did notice my players gravitating rapidly towards talking to things they encountered and finding clever ways around having to burn their combat resources.
I suppose this is really a continuation of yesterday's "don't reinvent the wheel" post, but I think older editions of D&D - or other games entirely, for that matter! - have a lot that's worth borrowing, stealing, or modifying in some way, even for the most modern games, especially to address something you’re not mechanically satisfied with at your table.
Feel free to dig around other game systems or editions to find an idea you like and want to try!
Hollow Dragon Tactics - The Monsters Know What They’re Doing
Skill Challenges for 5E, Part 4 - Kobold Press
d20 Plot hooks drawn from PCs' noble house (GLoGtober #8) - Seed of Worlds
I’m curious about OSR stuff in general - if you’ve had some experiences with it (especially which older/classic modules or systems/retroclones are must-runs), I’d love to hear your advice and suggestions!
Now get out there and tell a story!
Unless you use the variant milestone leveling, in which case you level up whenever the DM decides you do. But that’s another topic.