Ignore the ASBO comment.

Assuming you're not casuing excessive noise or noise at inappropriate times you'll be okay.

Just ensure you have a good (and quiet when hit) backstop and your pellets don't cross your boundaries you'll be fine.

Someone will probably post talking about 50 feet from any public highway. Ignore it, the offence is only complete if you endanger, iterrupt or alarm a member of the public on that highway. With your walls and being in your back garden you shouldn't have any problem with that.

Don't go out of your way to p|ss your neighbors off but don't forget it's your right to do what you like within the law within the boundaries of your own property.