Lots of really good feedback already in the post. Here's my experience:
I also live in the city, and our city ordinances are no roosters and max of 5 hens. Currently, I'm down to three - two silkies and a black australorp. When I was doing my research about noise factors and egg laying and docile natures, silkies were high on the list for docile and noise, not so great for egg laying. Australorps were supposed to be decent for noise and docile characteristics. Our backyard is larger than yours (I believe the house and yard are 1/3 acre if memory serves correct). But noise carries. Now, the caveat here is thusly: Darling neighbors on one side have an anxious dog and very loud dad but are superb people and they honestly can't hear the chickens, which shocks me. Folks behind them have a very young child that is on the spectrum and screams when things go awry. He has gotten better. However, the neighbors directly behind me have a rock band (I kid you not) and it's the drummer that lives there. They also have a 30 year old
Amazon parrot that when he screeches, it is LOUD, sounds like Jurassic Park, and my neighbors previously thought that it was living in OUR house! So when we got the chickens, despite my worry, they honestly aren't the loudest part of our busy little neighborhood.
That said, there's two instances that can be super annoying. One: The egg song. The girls want you to know they popped one out. It's important. And they are going to do so at the top of their little velociraptor lungs. And it can go on. And on. It's a natural part of their process, and it is LOUD. Usually these happen in the morning, but it can be any time of day.
Two: The intruder alert cacophony. If unfamiliar predators enter the yard (cat, hawk, racoon, dog, whatever), the hens will let out this insanely loud alarm song, something combined with the egg song and pretty much screeching, because their lives depend on it. I'm trying my best to not run out there right away, but rather look through the windows to make sure there's nothing I need to chase off. Because the girls are smart, despite it all, and I don't want them putting two and two together that if you make the alarm, mom comes out with treatos to shut you up. So there's that.
AND I almost forgot, the "I want to lay, get out of the damn nesting box Poppy otherwise I'll screech louder at you" sound. That one I actually find the most vexing (don't get me wrong, I love my girls!). Like, just get in there, push the broody girl over, and lay the damn egg for goodness sake! This, too, can go on for yet a few minutes to hours.
So if you're already having problems with the noise in your adjacent yards, chickens will most certainly be the thing that makes you snap. I'm so sorry. Do I love my hens? Of course. But I get it. Thanks for asking.