My son's kindergarten teacher has a great saying:
"Five year olds are very egotistical."
And she LIKES this age. Has been working with them for a long, long time.
What I read in some of your post seems like your daughter is protecting her ego. She knows what's happened and why she is receiving redirection or a consequence from you, but she doesn't want to rehash it. Much like a lot of adults, come to think of it.
When she says "I'm sorry" repeatedly, I would say "Thank you for apologizing. I really hope this doesn't happen again, for now we need to....." and let her know what comes next.
I have a rule with my son that "if you can show me with your actions that you want to make amends and fix this, I'd love to help you do that" and then we really focus on fixing the problem. At that point, if I see that he is genuinely contrite and wanting to fix the problem, there's sometimes a suspension of any consequential action. It really depends on if this is a first offense or repeat problem. I want him to learn how to fix his mistakes, and also, that many mistakes aren't irrevocable, but that we can learn from them and get past them.
Sometimes this is easier than at other times, too. When he's become overly emotional and near a tantrum, I do try to offer empathy to what's he's feeling frustrated/disappointed with and then, if he's still sounding unkind, I do just tell him "please go take a break until you are ready to use a friendly voice". I do believe that kids don't like feeling out of control, and that making him stay in his room for a specific amount of time is reserved for real rudeness, not just being angry at a situation. They are upset because they have no control, so taking away control further by insisting he stay in his room---when he might be upset and needing reassurance-- is really only for when he's being personal or unkind or purposely uncooperative.
Kids at this age DO NOT want to talk about their failings. This is really important to realize. They are no less vulnerable regarding this than we would be if we were at work and our boss had to censure us. What's worse, they feel terrible if we tell our spouses/others in their presence. My son has told me "please don't tell daddy" lots of times. This isn't about his wanting to be dishonest, but wishing he'd never made that mistake or wrong choice. It's just as bad as if we'd came out of the boss's office and they announced to everyone else "you'd better watch out for this one. She makes mistakes!" It's humiliating to their little egos.
I guess, when it comes to how I deal with my son, I try to think about how I would want to be treated and what I would have wanted as a kid. I would encourage you to parent from a place of hope, not fear. You have had a tough experience with your stepson, but it doesn't mean that your daughter is on the same path. She's five. I would encourage you to find a different response, because what we often hear when "sorry doesn't cut it" comes our way is "you can't fix this mistake. What you've done is so terrible, nothing can make it better. Your apology isn't good enough for me. I won't forgive you". You can relate to how terrible that made you feel. What did you *want* to hear from your father? "I hear that you are sorry-- let's try a way to fix this"? "Thanks for apologizing--you made a big mistake and I'm angry, and I still love you. We'll work through this"?
We want our kids to keep trying, so find a softer response to her apologies. You want a child who takes responsibility for her actions, so I would suggest finding ways, whenever possible, for her to make amends instead of being punished. She *will* learn better to fix problems she's created, to apologize (if it doesn't mean getting shot down or humiliated) when she's made mistakes, to approach her mistakes as often-fixable. If we only punish, we don't really teach them other than 'don't do it again'....we don't teach them the life skill of actually stepping up, taking responsibility and making things right. She has to trust that her apology will be taken at face value and that through making amends-- THAT is how she backs up an apology.
One of my pat phrases with my son, sometimes, is that when he apologizes to me after we've mended the situation, I'll tell him "thank you. You know the best way to show me that you are truly sorry?"
"Don't do it any more?"
"That's right, sweetie. Don't do it any more."
We're still working on a few things too. I won't lie and say we don't have some punishments-- he's going into a whole week of no treats because he snuck candy with a friend during a playdate at our home after another similar incident last week. Overall, though, he's a good kid and he's learning--learning that even when the older, more glamorous kid suggests sneaking something, he needs to say no. That's one I do have some fears about, and I have to remember that sneaking candy at five is different from stealing in high school. Natural consequences in the moment (like only getting to play in the living room for the rest of the playtime, with adult supervision) are part of the instruction, and so is our belief in them AND our message to them that we believe they can and will do better, eventually. (and yes, I sometimes think that a week of no treats will be a bit more instructive than 'being cool' with it. And he chose this from one of two "loss of privilege" choices he was presented with.)
Sorry this post is so long, but it's really not a "Do XYZ and your child will change" sort of thing. It's a lot more nuanced and I have no magic bullet answers.:) Walking down a similar path right now. Good luck and hang in there.