The fifth season of Dexter opened immediately where last season concluded: Dexter is outside his house, as the police arrive at the scene of Rita's murder and Dexter mutters: "It was me."
This causes the FBI to be a bit suspicious, while Dexter's subsequent behavior simply confuses Deb. She's doing all she can to help, such as make funeral arrangements, while her brother remains quiet and detached. As a result of this frustration, Deb ends up sleeping with Quinn (on the floor of Rita's kitchen!). Hot stuff.
Elsewhere, Dexter tells Astor and Cody about what happened and the former blames him. Dexter isn't sure what to do or how to react. He feels guilty over Rita's death, wishing he had killed Trinity much sooner, and starts to think the kids might be better off with Deb or their grandparents. From there, he actually escapes on his boat, planning to leave town.
But a run-in with some jerk in a convenience store bathroom leads Dexter to kill the dude in cold blood and for Harry to appear and say that's "the first human thing" Dexter has done since Rita died. He convinces Dexter that his family isn't better off without him, or vice versa.
The premiere concludes with Dexter showing up for Rita's funeral and giving a eulogy in which he says he wants to stay around Miami, to be near the people who loved Rita. This includes himself.