It turns out that the five countries alluded to in the New York Times story on the subject were Jordan and Yemen (which the Times named), and Syria, Algeria, and Indonesia, which for some reason the Times story didn't name. In more recent news, it turns out that India has also arrested a journalist for printing the cartoon. According to the story,

Alok Tomar, editor of Shabdarth, was arrested Wednesday after the government warned the Indian media not to publish anything that hurts the religious sentiments of any community.

I'm still not sure why the Times said there were arrests in five countries, but mentioned only two; I assume it was an editing error. But in any event, this is my attempt to fill that gap.