Modern horror ~ 5 to 6/10 that passed unnoticed

I found another one:
The Nun (2018) 5.3/10

Dark Water (2005) 5.6/10
This is what I'm talking about
I must find everything myself in this forum, you have no sense of good low-rated horror

No one lives (2012) 6/10

Luke Evans is great in this one.

I'm always keen to share and find great genre movies that didn't get the exposure they deserved, but as one poster noted The Nun had a huge box office. I keep it simple and use the number of IMDb votes as my metric for "popular" to "relatively obscure" aka "unnoticed." The four examples you give have vote counts of ~161K, ~138K, ~64K and ~11K, so I'll try ~20K as a good starting point and see if my search results feel "obscure/unnoticed" enough.

Now, as one who mostly ignores IMDb scores, especially for genre films, I'm a bit thrown off as to why anyone would deliberately want a lower-scored movie over a higher, if the only other criteria are genre and popularity. But since you asked, I'll try an advanced search and see if anything matching your score target is something I'd recommend. Barring that, I hope you'll forgive me throwing in a few higher-rated horrors that I feel deserve more exposure.

Anyway, I'll stop yapping and start recommending. Wow, there were more goodies that I expected matching your score range and my 20K vote limit. In fact some greats. More or less in order:

The Living and the Dead (2006) - IMDb rating 5.8/10, but it's a 9/10 for me. Really unsettling.

8/10 (my rating)
100 Bloody Acres (2012)
Det okända aka The Unknown (2000)
The Children (2008)

7/10
Baskin (2015)
Murder Party (2007) - Jeremy Saulnier's feature debut, and it's a blast. Unlike his darker, later films.
Frostbiten aka Frostbitten (2006)
Linkeroever aka Left Bank (2008)
Welp aka Cub (2014)
The Substitute (2007)
Benny Loves You (2019)
Kataude mashin gâru aka The Machine Girl (2008)
The Objective (2008)
The Broken (2008)
Alien Raiders (2008)
Isolation (2005)
The Borderlands aka Final Prayer (2013)
Bloodsucking Bastards (2015) - F'ing hilarious. Have watched well over five times.
Satan's Little Helper (2004)
Home Movie (II) (2008) - Chilling found footage gem

I'll stop there, and won't even open it up to higher IMDb ratings, unless requested, or I'd be here all day.

The watch party last night hosted Hatchet II (2010) and The God Inside My Ear (2017), the former a grisly grindhouse romp and the latter a trippy jazz-infused slow burn of madness. Both worth checking out!

Jennifer's Body 5.5/10 I recall it being a good film.
Carrie 2 4.8/10 haven't seen it and didn't know it existed. Just mentioning it as Carrie was in OP's post.

The Blackcoat's Daughter (2015).

IMDB rating is 5.9/10, but I'd rate it 8/10.

Look Away (2018)
Spoonful of Sugar (2022)
Dread (2009)
Wildling (2018)
Cam (2018)
Glorious (2022)
Honeymoon (2014)
Caveat (2020)