We report the discovery of the high-ionization [Ne v] λ3426 Å emission line in the spectra of five blue compact dwarf (BCD) galaxies. Adding the three previously known BCDs with [Ne v] emission, the entire sample of such galaxies now contains eight objects. The detection of this line implies the presence of intense hard ionizing radiation. Such radiation cannot be reproduced by models of high-mass X-ray binaries or massive stellar populations. Other mechanisms, such as active galactic nucleus (AGN) and/or fast radiative shocks, are needed. We consider that fast radiative shocks are the most likely mechanism. The observed [Ne v] λ3426/He ii λ4686 flux ratios in all eight galaxies can be reproduced by radiative shock models with shock velocities in the ∼300–500 km s−1 range, and with the shock ionizing contribution being ∼10 per cent of the stellar ionizing contribution. However, we cannot rule out that this 10 per cent part is produced by an AGN rather than by radiative shocks.