Hi, and welcome to the forum.
I'm not a lawyer by any means. So my sound advice might not be too sound, (yes lame dad joke). 1st. If the five chickens are all you have, no cats, dogs, etc, skip the rest of this paragraph. I agree with
@muddy75 , up to twelve is OK, but there are a couple "buts" to that ordinance. 1. Your property has to be zoned rural residential (You'll have to look at that on a zoning map, you should be able to find it online. It will probably easiest to find on your county's site.) 2. Your property must be over 20k square feet. (This should be on the same property map.) You can ask you mom to look at the deed or do a deed search online too. Those are the easy parts.
There is also at least one noise ordinance relevant. It basically states that the owner must keep an animal within what a reasonable person considers acceptable level. Vague for a reason, I am sure.
Here is what I would do,
Talk to your mom, show her the ordinances. As others have said, let her call the city and see what their take is before you even start to worry. (Make sure you are zoned and meet sq ftg 1st)
With your mom's blessing, for all of the following.
Get statements from all your immediate neighbors, if you have contact with the neighbor that moved who didn't mind, that would be extra good. This will go a long way for defining what a "reasonable" person finds too loud.
Set a phone out and get the neighbor's dog barking and your chickens being loud from the same spot, right on the property line. Get video, of where you place it, and showing the dog. Download a recorder app that will show the decibel levels. Good for the goose is good for the gander.
Pull up the local ordinances, bookmark them, take screen shots of the parts that are relevant. Have them ready, everything in one folder on your phone.
If you have contact with the police, or someone from code enforcement, health dept, etc, have your mom there with you,
be polite, but tell them why you think it's legal. Pull up the ordinances, state your case, show that your neighbors don't consider it a nuisance. Take notes of any code they cite.
Ask them what they think you could do to comply and still keep them. It's a good thing to video, just don't be obnoxious about it like some of the fartheads on Youtube, just tell them why.
Most normal people are going to be on your side, a teen raising chickens vs. zombying out to Roblox is going to get you empathy, if not support. Probably from the officer taking the complaint, among the first. Somebody who has an issue with a chicken clucking 30 feet away is probably going to rub plenty of people the wrong way. At the same time if they talked to your mom first, rather than calling the police, you may be able to work it out before it comes to that?
Option B. I truly despise the "safe space" culture that young people like yourself are being indoctrinated into. With that said, in this case, the ends justify the means. Get your mom to find you a sandal wearing doctor to document them as therapy animals, anxiety... whatever the reason. Let them try to take them then, or try and fine you. You'd have Non Profits and lawyers jumping to take your case for free so they could do their hours standing up for the disabled rather than defending a drug dealer. You could put one of your chickens on a leash and walk it in front of your neighbor's house after that, (on the sidewalk of course).

Your mom has legitimate worries. If your city has a third party lawyer, it is scary and wrong what they can do over a little code violation. I wouldn't blame her for not wanting to risk too much. You have county and state laws too.
If you have a 4H close, talk to them, they may have good advice, or an Ag or FFA teacher at school.
Good luck Kiddo, I'll put the ordinance link below.
(PS, find out what gets their dog barking, you want it going nuts if the police show up about your chickens. Don't make it obvious.)
https://library.municode.com/ca/lan...T17ZO_CH17.08REZO_ARTIVSTSPLAUS_17.08.180ANKE