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ABSTRACT We measure the mean free path ($$\lambda _{\rm mfp,H\, \small {I}}$$), photoionization rate ($$\langle \Gamma _{\rm H\, \small {I}} \rangle$$), and neutral fraction ($$\langle f_{\rm H\, \small {I}} \rangle$$) of hydrogen in 12 redshift bins at 4.85 < z < 6.05 from a large sample of moderate resolution XShooter and ESI QSO absorption spectra. The fluctuations in ionizing radiation field are modelled by post-processing simulations from the Sherwood suite using our new code ‘EXtended reionization based on the Code for Ionization and Temperature Evolution’ (ex-cite). ex-cite uses efficient Octree summation for computing intergalactic medium attenuation and can generate large number of high resolution $$\Gamma _{\rm H\, \small {I}}$$ fluctuation models. Our simulation with ex-cite shows remarkable agreement with simulations performed with the radiative transfer code Aton and can recover the simulated parameters within 1σ uncertainty. We measure the three parameters by forward-modelling the  Lyα forest and comparing the effective optical depth ($$\tau _{\rm eff, H\, \small {I}}$$) distribution in simulations and observations. The final uncertainties in our measured parameters account for the uncertainties due to thermal parameters, modelling parameters, observational systematics, and cosmic variance. Our best-fitting parameters show significant evolution with redshift such that $$\lambda _{\rm mfp,H\, \small {I}}$$ and $$\langle f_{\rm H\, \small {I}} \rangle$$ decreases and increases by a factor ∼6 and ∼104, respectively from z ∼ 5 to z ∼ 6. By comparing our $$\lambda _{\rm mfp,H\, \small {I}}$$, $$\langle \Gamma _{\rm H\, \small {I}} \rangle$$ and $$\langle f_{\rm H\, \small {I}} \rangle$$ evolution with that in state-of-the-art Aton radiative transfer simulations and the Thesan and CoDa-III simulations, we find that our best-fitting parameter evolution is consistent with a model in which reionization completes by z ∼ 5.2. Our best-fitting model that matches the $$\tau _{\rm eff, H\, \small {I}}$$ distribution also reproduces the dark gap length distribution and transmission spike height distribution suggesting robustness and accuracy of our measured parameters.