5th Edition mechanically wards off death as a mechanic.
Since it's a lot less likely that characters will instantly die in combat, it's less likely you'll have to deal with it as a DM. Here's a few reasons why:
Player HP Pools are higher
The smallest hit dice in 5e are d6 for unarmored spellcasters (Sorcerers and Wizards, specifically), and higher for everyone else. Along with monsters (generally) dealing less damage than they used to, this means player health pools tend to be less fragile than you might be expecting based on other editions of D&D. I don't know how it compares to non-D&D systems.
Death Saving Throws tend to make survival a lot easier
The way that falling to 0 hitpoints works in 5e is different to other editions. Here's the shorthand for the rules:
- If you fall to negative hitpoints equal to your hp total, you die instantly. (i.e., a level 1 character with 6hp takes 12 damage, drops to -6, dies instantly. If they took 11, they wouldn't instantly die)
- Negative hitpoints are truncated to 0, characters never persist at negative hitpoints (technically, negative hitpoints don't exist, but the rules are easier to understand if you pretend they temporarily exist at the moment you take damage, and then go away before the damage source concludes)
- While at 0 hitpoints, you roll a d20 at the start of each turn. 10+ grants a "save", 9- grants a "failure".
- 3 saves, and you're "stable" and no longer at risk of dying. No more rolls are made after this point.
- 3 failures and you die
- any healing in this state brings you back up, wipes all saves (succeeded and failed)
- a nat20 heals you for 1 hitpoint
- a nat1 inflicts 2 failures at once
The consequence for this system is that it's pretty rare for a character to straight-up die to one bad attack. It happens more frequently at low level, but as DM, you have the power to control the attack strength of your creatures, meaning it's unlikely anything will deal enough damage to one-shot anyone, even on a crit, unless you give them large damage dice. And since even the smallest amount of healing is enough to stave off death and get them back up, players don't need to use their most valuable healing resources just keeping a player alive. Paladins are especially good at keeping players alive, between giving bonuses to their Death saves, and having a pool of healing power they can spend in discrete, tiny chunks to keep creatures alive.
There's more options to revive dead players
At level 5, Clerics get access to Revivify (level 9 for Paladins, level 13 for Artificers), which can bring back a dead player so long as they died within the last minute. This gives access to revival magic a lot earlier than they would normally get it with Raise Dead (9 for Clerics and Bards, 17 for Paladins) or Reincarnate (9 for druids) or Resurrection (13 for Clerics and Bards), with the downside that it's more limited than any of those other spells.
All revival spells have a material cost associated with them, but by the time those spells are accessible, their associated material costs are (usually) plausibly accessible as well, depending on what sort of loot you distribute as DM.
You can always Deus-ex-Machina your players out of death
This is always a last resort, but if you make a mistake as DM (sending creatures that were too tough), you can find ways to undo death. Bring in a high-level mercenary to bail them out before the killing blows get struck, or have a celestial take pity on your characters. The more creative you are, the less contrived those moments will be.