Answer:
Very possibly. Cephalexin is not FDA approved for canines, but is often given as an "extra-label" med. Typical dosing is 10-15 mg/lb, tid or bid (2 or three times a day). Be advised this is a prescription medication.
Note that this med occassionally causes an allergic reaction which can be fatal in extreme cases. Also, not having the bacteria cultured means that this may not be the best antibiotic for this purpose -- you can't tell for sure without the culture.
Were it my pet I'd contact my vet and at least discuss it with them.
also it can be found in some toxic materials so make shure to take your dog to a vet and ask them first