You won’t find your 2005 Dodge Stratus battery stowed under the hood—it’s actually located behind the front driver’s side wheel well.
Unfortunately, this means that getting to your battery will take a good deal of elbow grease—not to mention requires you to lift your car up off the ground. Specifically, you’ll need to lift the car, remove the lug nuts on the driver’s side tire, then remove the wheel and tire. With the tires removed, you should be able to see the battery in the wheel well.
But if you’re not already familiar with the ins and outs of your vehicle’s wheels, or if your toolbox isn’t all too extensive, it may be better to defer to a mechanic for help replacing the battery.