Is it permissible to shake hands with a five-year-old girl or an elderly woman?

It is not permissible to shake hands with a non-mahram woman, whether young or old, due to the general prohibition by the Prophet, peace and blessings be upon him, against touching a woman who is not lawful to one, and because of his saying: "Indeed, I do not shake hands with women." As for a young girl who is not desired, and who is under seven years old, it is permissible to look at her and shake her hand.