Hello and welcome to just answer Jeep. I do not think that this is an alarm problem, because if it was, it would only run for about 2 seconds not 5 minutes. I believe you are experiencing either a PCM (engine computer) or crank position sensor failure. I recommend doing this: see if you can get a scan tool that will read codes connected to your Jeep. (rent one from your auto parts store if necessary). After it stalls, check to see if there are any codes related to "loss of crank signal" If there is, replace the crank shaft position sensor. If there are no codes, or the scan tool won't communicate with the PCM, then suspect a failing PCM. By the way, the only way to disable the factory alarm, is to remove the theft module, and then replace the PCM. This is because the PCM in your Jeep "knows that there is a theft module and will always look for it. If you disable the theft module, and not replace the PCM, then the Jeep will never start. Check the codes with a scan tool. This would be your next best move.
Hope this information helps, and let me know if you need more assistance with this,