Is my daughter teething?

I have a five week old baby girl who recently starting showing signs of teething. She gnaws, bites, sucks, and chews on her arms, fingers, and fists even when she is not hungry. She is also starting to drool. Instead of sucking her pacifier, she chomps down on it. She seems to feel soothed when I rub her gums. Is it possible that she could be teething?