Avian influenza A(H5N1) poses a public health risk due to its pandemic potential should the virus mutate to become human-to-human transmissible. To date, reported influenza A(H5N1) human cases have typically occurred in the lower respiratory tract with a high case fatality rate. There is prior evidence of some influenza A(H5N1) strains being a small number of amino acid mutations away from achieving droplet transmissibility, possibly allowing them to be spread between humans. We present a mechanistic within-host influenza A(H5N1) infection model, novel for its explicit consideration of the biological differences between the upper and lower respiratory tracts. We then estimate a distribution of viral lifespans and effective replication rates in human H5N1 influenza cases. By combining our within-host model with a viral mutation model, we determine the probability of an infected individual generating a droplet transmissible strain of influenza A(H5N1) through mutation. For three mutations, we found a peak probability of approximately 10-3 that a human case of H5N1 influenza produces at least one virion during the infectious period. Our findings provide insights into the risk of differing infectious pathways of influenza A(H5N1) (namely avian-human vs avian-mammal-human routes), demonstrating the three-mutation pathway being a cause of concern in human cases.