I think we'll have a flashback of the DOA4 events as an opening for the DOA5 story mode. We'll see Lisa working on her lab, like in the trailer, and probably short scenes like this to introduce Bayman and Helena and the ninjas (and the others), and someone's voice in the background (maybe Helena or Kasumi or maybe Mila, who knows) to explain what was going on at that time. That transition with Bayman's right eye is just.. a video editing, because it's cooler.
"War..is..terrible..it kills people.. some were mean (Lisa working)... people were mad.. blablabla... DOATEC was destroyed... some still wanted their revenge (Bayman's neck).. some wanted to start from scratch and rebuild it (Helena on her boat).. blablabla".
And if it's not that, well, I guess Helena will learn someday Bayman killed her daddy, so it's just a matter of time.