What is the ruling on killing stray dogs and cats?

The fundamental principle is that it is impermissible to harm animals, except for what has been explicitly permitted by religious texts, such as killing the "five noxious animals" and the black, purebred dog. Any animal proven to be harmful is also included in this category. However, even if an animal is permissible to kill, it is not permissible to torture it during the killing process. Furthermore, if its harm can be averted without killing it, then it is not permissible to kill it.