Adding a single mature rooster to a flock is one of the easiest additions. The only tricky part might be those two immature roosters. Probably the sooner you add him is better than later. The closer the two accepted members roosters get to maturity the more the chance increases for rooster fighting.
You may be able to run the 3 roosters in a flock of that size with them all getting along, and then again you may not. Some roosters do fine together, a great many do not, and there is little way to tell except to try it.
A 5 month old rooster is more mature than a 2 month old rooster, but neither are very mature when it comes to the hens. If I read you correctly, you only have immature pullets. All three roosters will be wanting to mate, long before the pullets are ready. Which is going to lead to a very stressed flock.
You are goiing to possibly have 3 rooster fighting to be dominant, and 3 roosters trying to bang anything that walks.
Depending on what your set up is, if you do not have some older hens, I think I would pull all three of the roosters and put them in a bachelor pad until your hens are much closer to 5-6 months.
You might put them all together and everything works fine, I don't thinks so, but sometimes that happens. AArt has often give this good advice about multiple roosters. Have it already set up so that you can immediately separate them. Because when it goes to hell, it does so fast, and you need to separate them fast.
Mrs K