How big (in feet or meters) is your coop? How big (in feet or meters) are the two runs? Just because it feels huge to you doesn't mean it is big enough for the chickens. How much room you have makes a huge difference in integration.
Where are you in general. My interest is in what your weather is like where you are. At five weeks old your chicks may well be ready to move outside now. Most chicks are fully feathered by that age and able to handle the weather but if you are having extremes in cold or wet that could affect it.
With my chicks they typically avoid the adults until the pullets start to lay. Until then I essentially have two separate flocks. During the day they stay where the adults are not. At night they do not sleep on the same roosts with the adults but stay away. I have an 8 feet x 12 feet coop and over 2,000 square feet outside. They have enough room to avoid the adults which makes integration a lot easier.
People with a lot less room go through integration all of the time, usually successfully. There are tricks we use to take advantage of what room we have. But I need to know what you have to work with to see what I might suggest.
My brooder is in the coop. Mine go in there straight out of the incubator or from the post office. Weather permitting, when mine are five weeks old I open the brooder and let them make their way with the flock. My integration is that easy. They were raised with the flock and they have room to avoid the adults. They know to return to the coop at night, since they were raised in there.
If your weather is OK and your coop is big enough, I'd suggest building a brooder in the coop and keeping them in there for a week before you let them out. You've already started the "look but don't touch" so this might be pretty easy. But what conditions are you working with?
My idea of a successful integration is that no one gets hurt. That's all. All the eating and roosting together and hanging together can come later when they nature more. As long as no one gets hurt, life is good.