I know a lot of players enjoy the appeal of 5E's high survivability rate, and much of it depends greatly on the DM's style, etc. but...
I find that, especially after tier 1, character deaths are few and far between, almost unheard of, and of course when they do occur recovering from them in many 5E games seems pretty simple with spells like Revivify. Even stabilizing is not that hard (the given mechanic is about 60% survival IIRC, even without aid). Exceeding your maximum HP after lower levels seems almost impossible in most situations for the insta-kill mechanic.
I've considered ways to make the game feel more deadly, such as imposing a level of exhaustion when you go to 0 HP, or giving a level for each failed death save (so even if you recover, you will need strong magic or some long rests to remove the penalties).
I was curious if anyone plays in a style of with house-rules that makes 5E more lethal to them?
Combat will near full HP should not be a terrifying experience (for the player anyway), but as HP dwindle and that 0 approaches, the player should understand their character is in danger and consider their options.
You do not need houserules per se to make 5e more deadly, what you do need is a good grip on how dangerous mobs with given abilities e.g.
attack chance / damage potential,
defense especially AC and HP and to some extent immunities,
tactics (how intelligent does a (group of) mob(s) act out,
offensive spellcasting ((AE/single target) blast or debuff/disable)
is to your given group. That includes knowledge on how your group mostly acts, do they go all in or do they often try to save resources. Do they have potions or other independent resources in addition to their character abilities. Do they ever flee and if yes will they leave party members behind.
In short, you need DM experience and a degree of system mastery.
Everybody just relying on the official guidelines is likely to either make things to easy or to hard, and this is ironically a weakness partially caused by one of the biggest overall strengths of 5E bound accuracy.
While bound accuracy keeps everything in line on one hand, one big boon or malus on whatever side weighs in the more. It is not the +1 to hit which will unbalance things nor the +3 to damage.
It is the mob/player gaining advantage almost all the time, or the +3 armor, or the heavy melee hitter with multiattack but a low CR despite of it which can ruin your fun.
Unfortunately I cannot give you any good hints on how to make 5e more or less deadly because it is all so relative and context driven.
For me personally as a DM I did my job right, if at least one party member is close to zero, and I did it best if one or more is in the death saves, but the party still wins the fight.
Not for every trash mob fight but for the big ones.
I rather reduce number of fights but make them meaningful.