How do you figure that? Half life doesn't mean that half decays in 5700 years and the other half decays in the next 5700 years. If means that half of what's left decays in the next 5700 years.
So, if half of the carbon 14 has decayed to nitrogen 14, then it's 5700 years old. If 3/4 has decayed, then it's 11,400 years old. If 7/8 has decayed, then it's 16,100. So half of a half of a half.... eventually it gets too small to measure, but not at 11,400. It's more like 50,000 years, I think.