With GE and no bags 2:54 is ample time to connect at JFK in your situation. No problems whatsoever. If things are on time you'll have at least 2 hours of lounge time before your JFK-LAX flight.

It's probably about the same amount of time to switch from T5 to T8 after arrival using the landside airtrain or going back airside in T5 and taking the shuttle. With that much time I would probably just take the airtrain since you're already landside.

AA Guide: JFK / New York J F Kennedy International Airport - MCT, Connection, etc