Improved theory of helium fine structure

Improved theoretical predictions for the fine-structure splitting of 2(3)P(J) levels in helium are obtained by the calculation of contributions of order alpha(5) Ry. New results for transition frequencies nu(01)=29 616 943.01(17) kHz and nu(12)=2 291 161.13(30) kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.