The current tracking system of the ATLAS experiment will be replaced by an all-silicon detector (ITk) in the course of the planned HL-LHC accelerator upgrade around 2025. The readout of the ITk pixel system will be most challenging in terms of data rate and readout speed. Simulation of the on-detector electronics indicates that the planned trigger rate of 1 MHz will require readout speeds up to 5.12 Gb/s per data link. The high-radiation environment precludes optical data transmission, so the first part of the data transmission has to be implemented electrically, over a 6-m distance between the pixel modules and the optical transceivers. Several high-speed electrical data transmission solutions involving small-gauge wire cables or flexible circuits have been prototyped and characterized. A combination of carefully-selected physical layers and aggressive signal conditioning are required to achieve the proposed specifications.