They offered me 10% more than the salary I said that I wanted. I want to wrap this negotiation up pretty quickly because they start date is soon, and I want to give my current job as much notice as possible.

Their standard benefits package includes 10 days of vacation accrued after the first year. I'd like to negotiate 15 days. How should I go about negotiating this?

Depending on where you are at, at times some benefits can not be changed, esp if they use or go though a outside pay management company. Often vacation or comp time is based on a certain amount per pay period added on.

But if you want to ask for it, you merely say you agree to all but >>>> and ask them for it