For structures that can be treated as networks of rigid, corner-connected polyhedra, the dominant distortion modes can be described by so-called rigid unit modes that are close to zero frequency. This type of behaviour is common in zeolitic/zeotypic materials such as the AlPO4 family of compounds and has been suggested by some authors to play a significant role in molecular diffusion within the pores of such compounds. We explore the energy and temperature dependence of these modes in AlPO4-5 using inelastic neutron scattering and heat capacity measurements. Ab initio based computational modelling is also used to assign the observed dynamic behaviour to rigid unit modes. We observe that these rigid unit modes persist down to very low temperatures and show no signs of freezing out.