Yes I see what you mean with your question... I too would hesitate on this one.
However, I agree with you that the simple past is more appropriate here. With the verb 'to arrive' you put the emphasis on the action of finally reaching the airport, which happened at a definite point in time in the (recent) past. Now if you want to insist on the impact and the connection with a present situation, then I guess you could use a different verb, one that could express the time that has elapsed since the event that constitutes her arrival.
In which case maybe you could say 'She HAS BEEN at the Kennedy Airport for five minutes now' or 'It'S BEEN five minutes since she reached the airport' or something like that ?

Pieanne wrote:

With "ago", you have to use the past simple. "Just" is different, you can use both. But when there's a precise time marker, it's always the past simple.

Students in my French classes had trouble understading how the passé composé could be translated to English with both the simple past and the present perfect.  I used your explanation of "precise time marker", and it seemed to help them understand their own language a little better.  "I've just done something" is an entirely different construction in French, so it posed no problems.