Hi Ann, The phrases "have lived" and "have been living" are very close in meaning. That's simply because of how the verb "to live" works (I mean, this certainly doesn't apply to other verbs). I'd use the Russian phrase which sounds most natural and logical to you. The thing to remember is this: when you use present perfect, you are talking about the present. If you still live in Moscow now, does the sentence, "Я жил в Москве 5 лет" still make sense? In English simple past ("I lived..."), I think the speaker doesn't live in Moscow anymore.

"have lived" is present perfect tense. It is neither past nor present but a combination of the two. It means the living "began in the past and has continued up to the present (and may continue into the future)."