Grammar Quiz explanation!

I lived in Rome. This means I don't live in Rome anymore.  This is the past simple tense.
 
I've lived in Paris, London and Los Angeles.  This means I know all these cities now.  This is the present perfect tense for past experiences with no time/date.
 
I've been living in London for 5 years.  This means I'm living there now.  The present perfect continuous tense is used to emphasize the length of time.
 
I'm living in London.  This is the present continuous tense - and it means that usually I live somewhere else, I'm only in London temporarily.  If London is your home, you would say I live in London.