they handle litigation, the attorney could be filing just to get $5,000 more from the litigation team. But depending on who your insured with, some roll over, and give extra money, some don't.
Most of the time, when attorneys go to file, I see one in four actually go to court. That's very anecdotal though.
Your insurance is supposed to defend you, they will appoint you an attorney if it goes to court.
Once it gets to the lit team, ask them what the last offer was, and what the last demand was. If the attorney is demanding less than your limit, you have little to nothing to worry about.