Etc light + esp bas + rough idle - 2005 Chrysler 300 Limited

have vehicle for trouble code

An Electronic Stability Program (ESP)/Brake Assist System (BAS) indicator is standard equipment on all instrument clusters. The ESP/BAS indicator is serviced as a unit with the instrument cluster.
The ESP/BAS indicator gives an indication to the vehicle operator when the Electronic Stability Program (ESP)/Brake Assist System (BAS) has been activated. This indicator is controlled by a transistor on the instrument cluster circuit board based upon cluster programming and electronic messages received by the cluster from the Controller Antilock Brake (CAB) and the Transmission Control Module (TCM) over the Controller Area Network (CAN) data bus.
The ESP/BAS indicator Light Emitting Diode (LED) is completely controlled by the instrument cluster logic circuit, and that logic will only allow this indicator to operate when the instrument cluster receives a battery current input on the fused ignition switch output (run-start) circuit. Therefore, the LED will always be OFF when the ignition switch is in any position except ON or START. The LED only illuminates when it is provided a path to ground by the instrument cluster transistor. The instrument cluster will turn ON the ESP/BAS indicator for the following reasons:

1. Bulb Test- Each time the ignition switch is turned to the ON position the ESP/BAS indicator is illuminated for about four seconds as a bulb test.
2. ESP/BAS Indicator Lamp-On Message- Each time the cluster receives an electronic ESP/BAS indicator lamp-ON message from the CAB indicating that the ESP/BAS system has been activated, the ESP/BAS indicator will be illuminated. The indicator remains illuminated until the cluster receives a lamp-OFF message from the CAB, or until the ignition switch is turned to the OFF position, whichever occurs first.
3. ESP Full Off Textual Message- Each time the cluster receives an electronic ESP Full OFF indicator lamp-ON message from the CAB indicating that the ESP/BAS system has been manually disabled, an ESP OFF textual message will appear within the cluster odometer display. The ESP OFF textual message remains displayed until the cluster receives a lamp-OFF message from the CAB, or until the ignition switch is turned to the OFF position, whichever occurs first.
4. Actuator Test- Each time the cluster is put through the actuator test, the ESP/BAS indicator will be turned ON, then OFF again during the bulb check portion of the test to confirm the functionality of the LED and the cluster control circuitry.

The CAB continually monitors the ESP/BAS circuits and sensors to decide whether the system is in good operating condition and the proper outputs to the components of the system. The CAB then sends the proper lamp-ON or lamp-OFF message to the Electro Mechanical Instrument Cluster (EMIC) (also known as the Cab Compartment Node/CCN).
For proper diagnosis of the ESP/BAS system, the CAB, the TCM, the EMIC, the CAN data bus or the electronic communication related to the ESP/BAS indicator operation a diagnostic scan tool is required. Refer to the appropriate diagnostic information.

yes

the operators manual is clear on that, did you read that first?
it says "get the car serviced" clearly
if you work on cars, do you? thne we scan the systems with the scan tool first. to see if there are complex hard errors.
like the ABS sensors, (not bas) sensor dead. (ops a road hazard hit it and broke the wire there, dang.
then if no hard failures.
first is not ESP (that be last dead last)
the first is , the brake must work perfect if not , the ABS can not
work correctly with bad brakes.
so check fuses.
scan ABS for errors
then do a full brake inspection, takes me 2 hours. but my guess,
youve never done brakes, right,, your self?
not even a full inspection?

1. leaks? (fluid)
2. pads worn out?
3. caliper pistons not sticking
4. rotors not cracked, or wrecked, surfaces.
5. caliper guide pins not seized. (they float free?)
6. emg, brake not sticking on partially?
7. wrong sized tires on car (or just one , omg)
8. ABS sensor parts damaged at axles ends.?
9. bad wheel bearing, seizing or loose.

etc... etc.... and more.

See a repair shop that does brakes. Be prepared to pay for a diagnostic fee to find problem.
That's an ABS light.

Have the brakes inspected for worn out brake pads causing a metal to metal scrape of the pad and brake rotor.

Any codes? Tune up, fuel filter, wires, coils, air filter, dirty throttle body, put seafoam fuel cleaner.

Try resetting the ESP/BAS system, with the car idling turn the steering wheel completely to the left then to the right then back to straight.

It will come on sometimes while driving in certain conditions, like a rough or loose road surface. It's indicating that the stability and antilock brake systems etc are in operation while those road conditions exist.

It will go out when normal road conditions are detected.

ESP = Electronic Stability Program
BAS = Brake Assist System