Hang Em' High
Many proponents of challenging DMing styles will praise the idea that a campaign world will be more engaging if the characters are at constant risk of death and dismemberment, but I'm not sure this is necessarily the case. Anyone that's skulked around the world of Dark Souls, nervously twitching at everything that bumps in the night, is well aware that it's not a pleasant place to vacation, nor is it a wonderful place to roleplay. In fact, the only optimal thing to do in a dangerous game (which is rather different than the real world, since you have no personal stake) is to kill anyone that gives you so much as a glance. NPCs are controlled by the DM, and the DM is out to kill you. Plus, there's the possibility that it's not really a normal person, but is a powerful spellcaster, or a monster of some variety in disguise. Better not chance it.
I believe that the solution is not a challenging world, but a dangerous one, a world where the lethality of encounters is difficult to predict, and where traps are less than consistent. We've talked about this before -- how players might respond better to a campaign world that isn't consistently game-y, which prevents player complacency and allows the DM to catch them off-guard. There's a much more entertaining dynamic when the party isn't convinced that they can survive any encounter, but also can't predict when real danger will show its face. Simply because bumping into some very dangerous monsters or into some especially lethal traps out of the blue keeps them on their toes, but doesn't keep them always at the ready. If done in the right ratio, the players should be more accepting of situations you put them into, and less likely to guess when the traps are coming.
The Best Defense is Powerful Magic
Now, another reason a dangerous campaign philosophy is acceptable is because of some quirks of the current edition, specifically dealing with magic items and other equipment. The vast majority of treasure in the DMG is only beneficial, and rather powerful. Magic items in this edition provide a static benefit with very few trade-offs or tactical limitations. Some of them are expendable resources, but many more are rechargeable, meaning your players are likely to employ them during every adventuring day. After a little bit of adventuring and some rolls on the magic item table, your party will start looking a lot more powerful than their level (and the CR of monsters) might suggest.
Moreover, damage is more negatable than ever, even in parties without a healer, due to the introduction of Hit Dice. You can mitigate the power that Hit Dice hold in your campaign by presenting sparer opportunities for rest, but the healing option remains, and players will be more difficult to outright wear down for that reason.
Therefore, harder-hitting, more dangerous encounters will probably be more appropriate to your party's level of play as they continue on through their adventures. You can play it easy at first, but once you've handed out some loot, it's time to take the gloves off.
Parties of More
In 5e, there's still plenty of options to play with NPC allies, be it summoned minions, or animal companions. The balance on these systems are far better than the previous editions, and Legendary Actions help to counteract the fact that your party will almost always take greatly more actions than their foes, but it's never quite enough. It can feel like parties of any size are invincible in combat. Especially when playing with 5 or more players (PC and NPC together), a very lethal, disable-heavy approach is key to keeping combat threatening. In such situations, hit half the party with debuffs to limit their effectiveness, while hitting the other half with enough damage to test their courage. This strategy always makes the party feel terrified, but no less able to succeed.
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