The exclusive ω electroproduction off the proton was studied in a large kinematical domain above the nucleon resonance region and for the highest possible photon virtuality (Q2) with the 5.75 GeV beam at CEBAF and the CLAS spectrometer. Cross-sections were measured up to large values of the four-momentum transfer (- t < 2.7 GeV2) to the proton. The contributions of the interference terms σ{TT} and σ{TL} to the cross-sections, as well as an analysis of the ω spin density matrix, indicate that helicity is not conserved in this process. The t-channel π0 exchange, or more generally the exchange of the associated Regge trajectory, seems to dominate the reaction γ* p→ωp, even for Q2 as large as 5 GeV2. Contributions of handbag diagrams, related to Generalized Parton Distributions in the nucleon, are therefore difficult to extract for this process. Remarkably, the high-t behaviour of the cross-sections is nearly Q2-independent, which may be interpreted as a coupling of the photon to a point-like object in this kinematical limit.