my limited research would indicate that, yes, she/we are indeed entitled to compensation.
* EU carrier leaving from an EU airport.
* Delay more than five hours on departure and just less than five on arrival.
* Delay was not weather or ATC related.
AB never stated it was a technical fault - though the fact that they kept moving the departure time back hour by hour leads one to think that it might have been, as they sought to locate necessary resources for repair. So, given those parameters, it seems to me worth waiting on an evaluation of the claim, rather than accepting the offer of AB's autoresponder.