The high entropy alloy which include all five magnetic 3d-transition metal elements CoCrFeMnNi (Cantor alloy), has a very complex ordered magnetic state at low temperatures. At elevated temperatures the Cantor alloy is in a paramagnetic state and the magnetic excitations and thermally disordered local moments are expected to play an important role. Here we investigate the influence of the magnetic order and longitudinal spin fluctuations at elevated temperatures on the elastic moduli of this alloy on the first-principle basis. We employ the Korringa-Kohn-Rostoker (KKR) method along with the coherent potential approximation (CPA), which is an ideally suited methodology to deal with alloys, in the framework of the local spin density approximation (LSDA) and disordered local moment (DLM) approach. We also combine this study with large super-cell calculations and ab-initio studies of the magnetic exchange interactions between different alloy components using the magnetic force theorem.