how to tell the new neighbors I shoot?
Introduce yourself - and hand them 5 bags of those cheap foam earplugs and say "You might need these. I shoot firearms and they make noise"
I had a neighbor come up one day when I was shooting one of my Freedom Arms 454 on my property (80 acres, borders a National Forest in a community of about 500 people). It's a loud handgun. She said some of the other neighbors were complaining and were going to call the Sheriff. I explained that what I was doing was legal, and that I was doing it safely and if she or they wanted to call the Sheriff I wouldn't mind. I then suggested she plug her ears because I had more shooting I wanted to do and it's loud. I don't shoot early in the morning or after dark.