  We study the constraints on reionization from five years of WMAP data,
parametrizing the evolution of the average fraction of ionized hydrogen with
principal components that provide a complete basis for describing the effects
of reionization on large-scale E-mode polarization. Using Markov Chain Monte
Carlo methods, we find that the resulting model-independent estimate of the
total optical depth is nearly twice as well determined as the estimate from
3-year WMAP data, in agreement with simpler analyses that assume instantaneous
reionization. The mean value of the optical depth from principal components is
slightly larger than the instantaneous value; we find tau=0.097+/-0.017 using
only large-scale polarization, and tau=0.101+/-0.019 when temperature data is
included. Likewise, scale invariant n_s=1 spectra are no longer strongly
disfavored by WMAP alone. Higher moments of the ionization history show less
improvement in the 5-year data than the optical depth. By plotting the
distribution of polarization power for models from the MCMC analysis, we show
that extracting most of the remaining information about the shape of the
reionization history from the CMB requires better measurements of E-mode
polarization on scales of l~10-20. Conversely, the quadrupole and octopole
polarization power is already predicted to better than cosmic variance given
any allowed ionization history at z<30 so that more precise measurements will
test the LambdaCDM paradigm.
