1999 BMW 528i problem?

In the morning when I start it it will idle for approximately 5-10 min then shut off. I will then restart it again and it will not shut off. If it is warm and I start it, it will stay idling. It is only stalling when it is cold in the morning. It is like clockwork every time. When I start it at first it is idling smooth and fine, but when it hits the 5 minute mark, it is like when your car is about to run out of gas. It sputters and is rough, then stalls. BUT, if I start it up in the morning and do not let it idle and I just go, it will NOT stall after 5 minutes. It is ONLY when it idles after initial start up.