We present a method to infer the role of selection acting during the within-host evolution of the influenza virus from short-read genome sequence data. Linkage disequilibrium between loci is accounted for by treating short-read sequences as noisy multilocus emissions from an underlying model of haplotype evolution. A hierarchical model-selection procedure is used to infer the underlying fitness landscape of the virus insofar as that landscape is explored by the viral population. In a first application of our method, we analyze data from an evolutionary experiment describing the growth of a reassortant H5N1 virus in ferrets. Across two sets of replica experiments we infer multiple alleles to be under selection, including variants associated with receptor binding specificity, glycosylation, and with the increased transmissibility of the virus. We identify epistasis as an important component of the within-host fitness landscape, and show that adaptation can proceed through multiple genetic pathways.