I say give it a shot, apply now - because while 5 years might be average, the minimums are usually 2 years, and with your internships and good GMAT score, make your profile pretty solid. And, if for some reason you do not get in, I don't think a failed application will hurt your chances at all.
And, somebody should correct me if I'm wrong, but I doubt your cousin's MBA will help you, unless of course she's in with the adcomm there and can put in a good word for you... A suggestion I would have is to try and put that in your essay, something along the lines of, "my cousin's experience at HBS motivated me to apply..." It can't hurt.
thank you all for your comments.
i know that for most of these schools the average work experience is around 5 years. by the time, i make my applications i will have only around 2.5 years of experience and 3 summer internship. Should I wait a year or two to increase my chances. and if I get rejected the first time I apply would that affect my future applications to the same school.
Lastly, my cousin had her MBA in Harvard a few years ago. Would that help my application to HBS?
Thanks all.