Introducing a new rooster to established roosters might be the difficult trick. They don't call it cock fighting for nothing. There is going to be a mad scramble to the whole pecking order, and who gets the hens, and who gets run off.
Generally - need several feed stations, maybe 4-5 places set up so birds eating at one, cannot be seen at another. Hide outs and multiple levels of platforms and roosts in the run have helped me.
A lot depends on where the new ones are now. I think that a big problem when integrating is the sense of territorial rights. Often times people put birds into a strange coop/run, and all the rest know they are strange, and so do the new birds.
I have had pretty good luck with letting the established flock out to wander around the yard. Locking the new birds IN the coop/run. Feed both groups along the fence line. Let them explore, find food and water without being chased for their lives. I would do this a couple days, and at night, I would put the new ones back where they were sleeping, let the established girls in.
3 days later, I would let everyone out of the coop/run but leave everything open. Keep an eye on them, but I would not expect much with 5 new ones, the more you add at one time, the easier it is. AND I would expect at least a few of them to follow the others back to the coop you want everyone in. Some of the new bunch might return to where they have been sleeping, but day 4 or 5, I would lock this up so nothing can sleep there, and toss any die hards into the floor of the coop I want.
This takes advantage of the fence around your coop/run that you already have. It is a bit of dinking around moving birds - but I have had very good luck with it.
However, I am positive this would work with your hens...not so sure about adding that third rooster... I think there might be a very good chance that this is not going to work real well. Generally speaking, the more roosters you have, the greater the chance of it not going well.
Why are you keeping that many roosters? You really don't need them for the number of birds you have?
Mrs K