Closing costs typically include: Lender fees, title company/recording fees, and mortgage/tax fees. In addition, you would need to come up with funds to establish an escrow account, which would be based on your actual property taxes and insurance.
In general, expect lender fees to be anywhere from $500 to $1500 depending on the lender you are using. Title company fees will probably run around $1200 or so. And the mortgage tax is probably going to be around $300-$350. You'll need to provide a full year's worth of insurance at the time of closing as well.
It's very concievable that the $5100 from the seller will cover all your remaining closing costs and escrows, but again it dpends on how much those taxes and insurance wind up being.
If you are looking for a lender and would like to talk about things in more detail please feel free to shoot me an email.