You can drive with a broken serpentine belt but only for a short distance just enough to get you off the road if possible.
I once had to drive my truck with a broken serpentine belt when it broke on the highway.
Luckily I was only about 1/2 mile from home and was able to drive for a bit and then when the engine started heating up I would shut if off and let it cool and then start it again and continue driving until I got home.
If I had to go longer than 1/2 mile then I would've called a tow truck as engine damage can occur and your battery will eventually drain as well and you have no power steering.
Now I always keep a spare serpentine belt with me and if it breaks I replace it before driving.
Serpentine belts last between 50,000 to 100,000 miles before needing replaced unless a bad pulley or misaligned pulley causes it to come apart.
If you notice cracks or wear on the serpentine belt it should be replaced and make sure the pulleys are aligned and not bent.
I always replace my serpentine belts at around 5 to 6 years regardless of mileage just to be sure it won't break on me and leave me stranded.
It's also a good idea to have a spare serpentine belt in your vehicle with you and the tools needed to replace it.
The signs that a serpentine belt needs replaced include.
Squeaking, squealing or chirping sound from under the hood of the car.
Check engine light or battery light is illuminated on your dashboard.
A/C isn't working.
Power steering isn't working.
The engine's temperature is high or overheating.
Smell of burnt rubber.
The average cost for serpentine belt replacement is between $109.00 and $134.00
Labor costs are estimated between $57.00 and $72.00, while parts range between $52.00 and $62.00
Whether you go to the mechanic or do it yourself, replacing a serpentine belt costs $58.00 to $126.00
Although you can sometimes get a cheaper serpentine belt online such as through eBay.