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Ab initio calculations in few- and many-body systems require precise two-nucleon forces as input. We present new precise nucleon-nucleon (NN) potentials up to fifth order in chiral effective field theory, whose adjustable parameters have been fitted to the 2013 Granada database of experimental NN scattering data. We discuss the removal of redundant contact interaction terms and a new local regularization scheme for long-range forces in momentum space. Last but not least, we study the effects of sixth-order contact interactions in F-Waves in the two-nucleon system.