No, I think you did well. If you have decided on a range that you would be pleased with and that is the first offer you should take it. At that point, if it come down to it, you are no longer willing to walk away.

Remember when you were happy with the 5K? This was because the negotiation actually came in at 50-50 split: You were happy with X, but were reaching for X + 15; they were willing to go up to X + 10, but were hoping for X.