The Global Ozone Monitoring Instrument (GOME) was launched in April 1995 on ESA's ERS-2 platform, and the GOME Data Processor (GDP) operational retrieval algorithm has produced total ozone columns since July 1995. We report on the new GDP5 spectral fitting algorithm used to reprocess the 16-year GOME data record. Previous GDP total ozone algorithms were based on the DOAS method. In contrast, GDP5 uses a direct-fitting algorithm without high-pass filtering of radiances; there is no air mass factor conversion to vertical column amount. GDP5 includes direct radiative transfer simulation of earthshine radiances and Jacobians with respect to total ozone, albedo closure and other ancillary fitting parameters - a temperature profile shift, and amplitudes for undersampling and Ring-effect interference signals. Simulations are based on climatological ozone profiles extracted from the TOMS Version 8 database, classified by total column. GDP5 uses the high-resolution Brion-Daumont-Malicet ozone absorption cross-sections, replacing older GOME-measured flight model data. The semi-empirical molecular Ring correction developed for GDP4 has been adapted for direct fitting. Cloud preprocessing for GDP5 is done using updated versions of cloud-correction algorithms OCRA and ROCINN. The reprocessed GOME GDP5 record maintains the remarkable long-term stability of time series already achieved with GDP4. Furthermore, validation results show a clear improvement in the accuracy of the ozone product with reduced solar zenith angle and seasonal dependences, particularly in comparison with correlative observations from the ground-based network of Brewer spectrophotometers.