You left out an entire pillar of stuff to be afraid of that makes taking a small 3-5hp hit something that can create some fear even if taking several more that would drop the PC to that 0-5 razor's edge range you note as an area of fear. That omission is one 5e primes players to ignore by design though.
Prior to 5e PCs died at zero (or neg10 with the death's door optional rule) and every single point of damage needed to be healed at a
situational day by day rate and spell slot by spell slot and without unlimited cantrips while lacking full BaB progression the cleric wasn't going to be keen on dumping all of their slots healing
everyone back to full. Sure they might burn a couple bringing the tank back to the upper 80% or so, but they aren't going to and generally couldn't top off everyone. That led to the situation where a 2-3 point hit to the wrong PC could be scary because the player knew their cleric couldn't waste the heals on them when they might need it for the tank later.
Fear in PCs requires that the system present plausible risk like that to the players coupled with a hunger for more. Will our resources hold out? If we work together better and really stretch can we get MOAR of the phat lewtz we know that we really need and bigger experience payoffs? Can our carrying capacity carry all of the supplies and equipment we expect to need?... Obviously not... Which do we need now and which can we plan to go without? How can we stretch each HP of life?...
With 5e we have endless discussions over useless storytelling concepts like "horror" and "[narrative] fear" because the system now answers all of those questions with "easily but you shouldn't need to!" and " of course who cares?" while effectively ensuring that the PCs don't actually mechanically require anything they might narratively "need" to remove that hunger side of the formula.
As long as the system designs against it, why are we asking how the gm can generate fear in PCs instead of asking why the system itself lacks anything that should provide plausible reasons to be convincingly having PCs feel fear?