I had my period from Feb 1-5 and then I got it again on Feb 16 is it possible that I'm pregnant?

Assuming you had a full, normal period between 2/1-2/5, you should not have a period again so soon instead you may have spotting (light bleeding) since this is the time of your cycle in which you should be ovulating. (this time occurs 14-16 days after the first day of your previous period.)

Spotting during ovulation is normal and is a sign of fertility, though it is so light that it usually goes unnoticed. You should not be experiencing a full blown, heavy flow period only 12 days after the conclusion of your last period, if you are, I suggest you consult your physician. Better safe than sorry.

It is extremely unlikely that you are pregnant unless you had unprotected sex between Feb 13-today*, estimated based on the average female cycle. Take an over the counter pregnancy test, just to put your mind at rest.