You should talk to an attorney who handles juvenile matters.
What will happen depends, in part, on whether or not you have been in trouble before. If so, what were you in trouble for and when.
The court could have you confined for up to six months and require that you pay a fine upto $1,000.00 plus what are called impounds and other assessments.
If you have no record and the item only cost $5 dollars, there is a good chance you will get some sort of a diversion type program and be able to avoid a conviction. I always advise to error on the side of getting an experienced attorney to make sure you do not end up with a conviction. This may happen without an attorney's help...
If this is the first time you have been charged with a crime, there's a good chance that you will get an opportunity to have the case dismissed. In juvenile delinquency court, there's 654 informal probation. Basically, you go to court. You do not have to admit the charge as true. You can deny the charge, and for a period of around six months you stay out of trouble and pay the restitution ($5.00 or whatever it's worth) and listen to the probation department. There might be a theft class or something that you have to do in LA County. It should be a simple process. You would have to go back to court after six months and the judge and DA would determine if you did everything you were supposed to do. If you did, the case gets dismissed.
You will have to go to court even if the owner doesn't want to press charges. In fact, the DA can still prosecute the case even if the owner doesn't want charges. I don't think a minor case like this will get that far. Assuming it's a simple shoplift and you don't have a record or haven't been charged before.
Even though you are in LA, a juvenile file will follow you to whatever county you go to. For example, if you commit a crime in Riverside, the Riverside court will know about LA even if the LA case is dismissed. If you were to commit a shoplifting offense in Riverside after this case is dismissed, you would not get 654 informal probation. You would get a tougher sentence and it would be on your record.
Make sure you show up to court. There's no bail for minors. Good luck.