Considering that a lot of innocent people are murdered by the state via jury and trial in the US the distinction isn't very clear imo.
~211 people were killed via trial sentence in the US in the last 10 years [0]. Presumably some of them weren't innocent. In the same time period (conservatively) 8500 were killed by law enforcement outside of the legal process [1].
Both are problematic, but calling <20 people/year (out of a third of a billion people) "a lot" is missing the forest for the tiny sprig of moss.
[0] https://deathpenaltyinfo.org/database/executions?year=2024&y...
[1] https://en.wikipedia.org/wiki/Lists_of_killings_by_law_enfor...
Is 5 a lot?
Depends. Potatoes? No. Murder? Yes.
For example, we can go into treacherous schemes that pushes our neighbors into paths where the only obvious option they can still perceive as a way to escape our shenanigans is an attempt to kill us, and as they come with this very real intention to kill us, press the button we had prepared to trigger some mortal trap.
Making prevailing the idea that some humans can reach a level of certainty that is high enough to put a death sentence on some people they didn’t even knew before that is telling a lot. Like, we humans never make errors, we don’t have any kind of cultural and idiosyncratic biases, we never have conflict of interest and we can’t be manipulated by miscellaneous social forces.
Murder is bad, and murder en masse committed through institutionalized legitimating mechanisms is thus extremely bad, as as many times as bad as how many people it kills.
Legal murder through institutions never prevented a society to have "random" citizen going awry and kill other people, but it never missed to add supplementary threats to all their citizen.
It's quite possible for someone to hold that a killing in self-defense is much more defensible than the deliberate execution even after a conviction and trial of someone who is "no longer harmful to society" because they're locked up.
But a murder carried out by a random citizen is still worse than a death sentence after a fair trial and convicted by a jury of your peers.