Since the movies aren't actually numbered and should be enjoyed simply for what they are, the order goes: Resident Evil, Apocalypse, Extinction, Afterlife and Retribution.
Resident Evil: Retribution reportedly cost $65 million to make and grossed $221 million worldwide. Yes, Michelle Rodriguez was back in it. Yes, it was somehow explained. No, we can't recall the reason. Clearly we aren't on the same page on how these movies should be enjoyed.