Global disease suitability models are essential tools to inform surveillance systems and enable early detection. We present the first global suitability model of highly pathogenic avian influenza (HPAI) H5N1 and demonstrate that reliable predictions can be obtained at global scale. Best predictions are obtained using spatial predictor variables describing host distributions, rather than land use or eco-climatic spatial predictor variables, with a strong association with domestic duck and extensively raised chicken densities. Our results also support a more systematic use of spatial cross-validation in large-scale disease suitability modelling compared to standard random cross-validation that can lead to unreliable measure of extrapolation accuracy. A global suitability model of the H5 clade 2.3.4.4 viruses, a group of viruses that recently spread extensively in Asia and the US, shows in comparison a lower spatial extrapolation capacity than the HPAI H5N1 models, with a stronger association with intensively raised chicken densities and anthropogenic factors.