The continuing pandemic threat posed by avian influenza A/H5N1 viruses calls for improved insights into their evolution during human infection. We performed whole genome deep sequencing of respiratory specimens from 44 H5N1-infected individuals from Indonesia and found substantial within-host viral diversity. At nearly 30% of genome positions multiple amino acids were observed within or across samples, including positions implicated in aerosol transmission between ferrets. Amino acid variants detected our cohort were often found more frequently in available H5N1 sequences of human than avian isolates. We additionally identified previously unreported amino acid variants and multiple variants that increased in proportion over time in available sequential samples. Given the importance of the polymerase complex for host adaptation, we tested 121 amino acid variants found in the PB2, PB1 and PA subunits for their effects on polymerase activity in human cells. We identified multiple single amino acid variants in all three polymerase subunits that substantially increase polymerase activity including some with effects comparable to that of the widely recognized adaption and virulence marker PB2-E627 K. These results indicate highly dynamic evolutionary processes during human H5N1 virus infection and the potential existence of previously undocumented adaptive pathways.