You should be using "has been"
"It has been five years since he lived here."
I would have said "He moved away five years ago" but "It has[already] been five years since he moved" works if you said it.
Do they mean the same thing? Almost -- if you were talking about a residence where the person lived then I would say they do imply the same message. There might be some confusion in the second case if both you and the listener aren't clear about the location (home, city, country).
Not a teacher -- AmE native
Student or Learner