I am an Application Developer applying to jobs. Would you throw my resume out if you saw that I had 5 jobs in the last 4.5 years with the longest being 1.5 yrs? 

The back story on this is that I moved a lot because these jobs were while I was in college. I was able to move up very quickly by changing jobs. However, I do not want a recruiter to be thinking about this because these were all full-time jobs (back to back) and perfectly legitimate experience. However, by listing them, I'm afraid my resume will get tossed because they will think I just hop jobs every year.

My only saving grace is that I am not looking to leave my current job because I don't like it. I am trying to move out of state. I stated in my summary that I am looking to relocate. My hope is that most people are not too shocked by this because it seems fairly common in IT.