At five weeks, your chick is old enough to begin integrating into the flock. At the beginning, it will lack self confidence and will be fearful of the adults. But since you've had the chick in proximity to the flock, it has been accepted as a flock member pretty much.
What you need to do to give your chick the boost of self confidence it needs to integrate is to provide it with a safe refuge. Set it up in the run or where the flock spends the most time during the day. Create a small safe pen with two or more 5 x 7 inch openings so the chick can scoot back inside when it becomes fearful of the adults. Place food and water inside where the adults can't reach it by sticking their heads into the openings.
Over time the chick will need this "panic room" less and less. Usually by the time it's two months old, integration is all but complete.
You can get rid of the tub inside the coop and the light. The chick won't need it if it's spending its waking hours in the run. At night you may need to teach it to go back inside the coop to sleep. You can provide it with it's own space or wait and see if it will use a perch. I transition my chicks to coop sleeping by placing a cat bed inside in a corner for them to sleep in. It's a cozy and reassuring place for chicks to sleep and in a few weeks, they usually start using the perches on their own.
Don't worry about the chick's safety at night. Chickens are more intent on settling in to roost than they are in bullying a chick.
