Comparison of SN 2005hk and our N5def models with 0.01%, 0.22%, and 36% helium abundances. Optical and infrared spectra have been normalised to the median flux from 5000 Å–7000 Å and 10 000 Å –12 000 Å, respectively. The optical and infrared spectra of SN 2005hk are approximately +13 days after B-band maximum and have been corrected for galactic extinction only. Our N5def model is shown at +15 days after bolometric maximum light. Panels a and b: shaded regions represent He I λ5876, λ6678, λ7065, λ10830, and λ20587 at rest and blue-shifted by the maximum velocity of the model (∼12 300 km s⁻¹). Panels c–g: zoom-ins of the regions surrounding He I λ5876, λ6678, λ7065, λ10830, and λ20587, respectively. Rest wavelengths are denoted by a vertical dashed line.