We present spectral energy distributions (SEDs) for 86 Herschel sources detected at 5{sigma} at 250, 350 and 500um in the HerMES SWIRE-Lockman field. We explore whether existing models for starbursts, quiescent star-forming galaxies and active galactic nucleus dust tori are able to model the full range of SEDs measured with Herschel. We find that while many galaxies (~56 per cent) are well fitted with the templates used to fit IRAS, Infrared Space Observatory (ISO) and Spitzer sources, for about half the galaxies two new templates are required: quiescent ('cirrus') models with colder (10-20K) dust and a young starburst model with higher optical depth than Arp 220. Predictions of submillimetre fluxes based on model fits to 4.5-24um data agree rather poorly with the observed fluxes, but the agreement is better for fits to 4.5-70um data. Herschel galaxies detected at 500um tend to be those with the highest dust masses.