Probably not.
Two issues. First, a primary fermenter wants to be bigger than five gallons (unless you are making a 4 gallon batch, you need room for the krausen. Second, most of those bottles allow a very high amount of O2 to pass through, which can have a severly detrimental impact on flavor. Check the bottom of the bottle; if the number in the recycle symbol is a "7," it's no good to you as a fermenter, it's just "other plastics", meaning that it could be pretty much anything.
If it's a "1" (unlikely but possible), that means the plastic type is PET, which is fine for a fermenter. You should still get something bigger for a primaries (food-grade buckets are dirt-cheap), but the water bottle might be OK for a secondary fermenter (also known as a clearing tank).