I wrote the stuff below for a different thread so it does not fit your situation that well, but it gives some general information I think might help you.
A broody hen will often wean her chicks and leave them on their own with the flock at 4 weeks so they can be integrated at that age. The younger they are the more risks and I’m not a broody hen. I wait a little longer.
I think how much room they have has a lot to do with it. Chickens have developed ways to live together in a flock. One of those ways is that the weaker runs away from the stronger if there is a confrontation or just avoids the stronger to start with. They need enough room to run away or avoid.
There are a few things you have to worry about. One is that chickens can be territorial. They recognize which chickens belong in their flock and can attack strange chickens. There is a big difference in what can possibly happen and what will happen each and every time. Sometimes this is not a problem at all, but it is often enough to be a legitimate concern. A good way to help out on this is to house them side by side but with a fence between them so they can get used to each other’s right to exist but cannot get at each other to attack. Usually a week is enough but there is nothing wrong with longer.
Then you have the pecking order. For the flock to exist peacefully each chicken needs to know its social rank. They establish this by intimidation, pecking, or fighting. If a chicken invades the personal space of another and they don’t know how they rank or if there is a challenge to change that pecking order status, one will peck the other or in some way try to intimidate it. If the weaker runs away, the pecking order is established and everything is again peaceful. There may be some chasing and running away involved, but as long as there is space, things are well. But if one does not run away, it’s a challenge and can get pretty violent, maybe even deadly. So they need adequate room to run away.
A mature chicken always outranks an immature chicken and is usually not very slow to enforce and protect that rank advantage. I’ve never had a mature dominant rooster harm a chick in any way, but it’s pretty normal for some hens to be brutal about this. Some hens seem to go out of their way to harm a young chick. If they have space, a chick old enough to take the weather can do OK with the flock, but the tighter the space the more at risk they are. If your space is really tight, you may need to wait until the young ones are grown before you try to integrate them, and even then it can get really messy.
Maybe a story will help put this in perspective. I’ve seen several occasions where a chick maybe 2 weeks old being raised with a broody with the flock leaves the broody hen’s protection and goes to stand beside the other adult hens at the feeder. Sometimes the other hens ignore that chick entirely but it usually does not take long for an adult to peck the chick to remind it that it is bad chicken etiquette for it to eat with its social betters. The chick goes running back to Mama with wings flapping and peeping its head off. Mama generally ignores all this, but if a hen starts to chase the chick to drive that message home, Mama gets all kinds of bad attitude and teaches that hen to not threaten her chick like that.
My brooder is in the coop. They see each other from the start. I have a grow-out coop and run that is next to the adults. I have a lot of space in the main coop and outside. At about 8 weeks I let them out to range together. The young ones still go back to the grow-out coop to sleep. Usually around 12 weeks I move the young ones in with the adults. I put in an extra roost lower down and separated a bit from the main roosts so they can sleep further away from the adults if they want to without going in my nests. I have yet to lose a chick doing it this way, which means I’m probably being over-cautious.
Other than provide as much space as you can, it really helps to provide separate eating and drinking stations so the young can eat without challenging the older. Having things they can hide behind or under can help them avoid the older birds. What you will normally see is that they form two separate flocks during the day. They need room to do that.
Growing chicks should not eat Layer feed. It has excess calcium in it that tests have proven can seriously harm growing chicks. In these studies they cut the chicks open to see what the excess calcium does to the chicks' organs. It’s not pretty. It’s not how much calcium is in one bite but how much calcium they eat in a day on a regular basis that does the damage. If the chick gets most of its food from foraging, the extra calcium in the little amount of Layer it eats is not as likely to hurt it as if it eats nothing but Layer.
The way I get around this problem with a mixed age flock is that I feed them all the same feed, Starter or Grower, and offer oyster shell on the side. This way the ones that need the calcium for egg shells get it from the oyster shell and ones that don’t need it won’t eat enough to harm themselves.
As you can see from this, there is not one perfect age to integrate chicks. What works for you will depend in your specific flock (whether you have a brute of a hen) how you manage them seeing each other, how you feed them, and especially your space. Good luck on determining what is right for you.
For your specific circumstances, I’d be real nervous adding just hatched chicks to 5 week olds. It might work out or you might have a massacre on your hands.
The five week olds are pretty darn big compared to newly hatched chicks and should be getting pretty ready to go outside without heat, depending in where you live. The young ones will still need heat. Due to their different needs, I think you will be better off brooding them separately and integrating them later. But if you can keep then side by side for a while, your chances of success go way up.
Good luck!