Five weeks is too much of an age spread. I wouldn't put the older chicks with the new hatches for a couple of reasons. Baby chicks will be overwhelmed by the size difference, which will be considerable, much more than quadrupled by the larger chicks.
And the other reason is it takes at least three weeks for new baby chicks to learn about and understand how to relate with bigger chickens, young or older, and to cope with the pecking order. They simply aren't equipped before then.
I would, however raise them side by side in full view of one another so they do have the opportunity to learn and to relate, then you can begin to let them mingle after the new chicks indicate they're ready, between three and four weeks old.
It's also a good idea to raise all of the chicks in full view of the adult flock if there is one, for these same reasons, making integration much easier when the time comes, utilizing a "panic room" with small chick size openings for the smalls so they have a safe refuge from the larger chicks and chickens.
One of the most challenging issues with integrating smalls with bigs is the food. Larger chickens often chase the smaller ones away from the food so they have a hard time getting enough to eat. So you put the food inside the panic room and they have a safe place to eat as well as to rest up from being hassled.