Had the E05 error on my Hoover Optima OPH714D.  Replaced the NTC probe thermostat (approx £12) and has been fine since.  Not sure the part was faulty, but was heavily limescaled, so may be worth checking that before you buy a new one.  Very easy to access & replace, 2 screws and remove a wiring clip.
                 Martin
                
 December 2010