62 views and no advice? Ok, I'll bite.
I have a few thoughts on this so I'll just list them in no particular order:
You met and moved yourself and your daughter in with this guy pretty fast, according to you. So now some virtual stranger has moved into this kid's home, bringing changes and another kid, and taking up Dad's attention. That has to cause some ripples.
Whatever people say, and there are always exceptions, girls and boys in general mature at different rates and can be very different in their energy levels. In my group of friends, we are split evenly between boys and girls around the same ages. The girls could more or less sit still and play quietly fairly early. Don't get me wrong, they can also be WILD but in general, if we are inside, we can say hey, girls, keep it down - and they do. The boys will be actually figuring out how to climb the walls. The boys are still working on it. They can be nothing but noise and motion a lot of the time and I think that's just kinda how boys are. It's not good or bad, it just is. Your expectation that this younger boy should be just like your daughter is unreasonable.
Kids, when thrown together, will have conflict. Your daughter might have been really well-behaved in the past mostly because she didn't have another kid to have conflict with.
Five year olds in general aren't super aware of other people's feelings. They are working on it. They are learning empathy.
I don't think that tv, junk food, and some late bednights necessarily = bad kid. I think he's been raised very differently from your parenting ideals and you've decided that's the root of his problem. The most likely things are a, he's a kid and he's full of energy, b. he now has competition for his dad's attention, and c. you're making a lot of changes in his life.
Personally, I would back off and live in my own house if that's an option. Back off, cool off on staying there so much, and work on having the kids not on top of each other all the time. Let him have his space back, start over, and ease into it. It sounds like too much, too fast, for having kids involved.
It's not exactly the same, but I do have a similar experience. My own daughter is almost nine. Her cousin is two years younger. Last year, due to divorce, Cousin was suddenly with us ALL THE TIME. These kids love each other and they were still SICK of each other. They are both onlies who are used to down time and having their own space and their parents to themselves. Suddenly, there was conflict. My own well-behaved, easy going child was suddenly a wreck, and Cousin was doing everything in the world to get her attention - copying, knocking things over, being bossy and demanding. It was just too much of them together too often. A year later, things have settled down and Cousin doesn't have to be here so much, but I wish we could have a do over on the beginning of the year. We thought because they were both kids of a similar age and because they were buddies, it would all be fine. WRONG. Our expectations were just way, way off. What the kids were going through was normal and even predictable if we had actually been THINKING, but we weren't.