Mike, paying $5100 a year in insurance is extremely high, I know people with DWI's paying less than that!
Now, you said you'll get added onto your familys plan, but are they going through esurance.com also? You have to get the quote from your familys insurance carrier, when you went to esurance they probably expected you to be the only one. See what discounts your familys carrier will offer, good student, multi-vehicle household, ect. Also, even if you family is happy with the carrier and isn't going to switch, it doesn't hurt to get quotes from others.
Like Wetzel said, the vehicle makes a big difference also. My first car was a used 4cyl Dodge Omni......your basic entry level car. My insurance (Nationwide) wasn't even half of your quote. For ha-ha's try redoing the esurance quote but use a 2001 Chevy Cavalier instead and see what it is.