While parental H5 HA exhibited limited binding to human tracheal epithelium, introduction of selected mutations converted the binding profile to that of a current human influenza strain HA. Strikingly, these amino-acid changes required multiple simultaneous mutations in the genomes of naturally occurring H5 isolates. Moreover, H5 HAs bearing intermediate sequences failed to bind airway tissues and likely represent mutations that are an evolutionary “dead end.” We conclude that, although genetic changes that adapt H5 to human airways can be demonstrated, they may not readily arise during natural virus replication. This genetic barrier limits the likelihood that current H5 viruses will originate a human pandemic.