First of all, any time you bring home a new bird, they absolutely need to be quarantined away in a totally separate room from any birds you already have in your home for at least a 30-day quarantine-period. This is the only way to protect your already healthy birds from catching any bacterial/fungal infections, parasites, and/or avian diseases that the new birds may have/be carrying, especially if the new bird(s) come from a pet shop or a breeder that has lots of other birds. So you should NEVER just put them together with birds you already have...
Forgetting the necessary quarantine, I don't know what your actual "housing" situation is with your birds, you ideally each of your birds need to have their own cage, or at least the pairs that know each other and are comfortable with each other need to have their own, individual cages with their own toys, food and water dishes, mineral blocks, cuttlebones, etc. The two Cockatiels that you already had and that are bonded to each other and living together do not know these new birds, and they are not just going to automatically be comfortable with them. You need to keep them separated in their own cages and slowly, gradually let them get to know each other.
After the initial 30-day quarantine period you can put their cages in the same room with each other, so that they can see each other and talk to each other, and slowly get used to each other, and only allow them short time periods out of their cages together that are supervised by you. THERE IS NO GUARANTEE AT ALL THAT ANY NEW BIRDS YOU BRING HOME WILL GET ALONG WITH THE BIRDS YOU ALREADY HAVE, OR THAT THE NEW BIRDS WILL GET ALONG WITH EACH OTHER EITHER! Birds are very much like people in that they like some other birds, they dislike some other birds, they bond closely to some other birds, and they are aggressive and violent with some other birds. And there is no way to anticipate how they are going to get along, nor can you ever force them to get along, it just doesn't work that way! And if some or all of these new birds you just brought home don't like the two birds you already had, or vice-versa, then that's just how it's going to be, and you'll have to keep them separated and supervise them at all times according to how they eventually get along with each other...But again, this should be a gradual, slow introduction, you cannot just bring home new birds and go "There ya go, be together", obviously as you're seeing that doesn't work...and as a result, the two birds you already had are feeling uncomfortable, unsafe, and territorial about their cage/toys, etc.
****Also, if the 4 Budgies that you just brought home were housed together at the pet shop or the breeder, and they get along, then that's fine, you can put them in the same cage together as long as the cage is large enough to house 4 Budgies comfortably along with lots of toys, dishes, etc. However, the new Cockatiel you brought home was most-likely not housed together with the 4 Budgies either, so he needs to also have his own cage, and you can't just throw him in together with 4 Budgies, as this is exactly how tragedies happen...And the same thing goes for the two Cockatiels you already had, you absolutely cannot just throw them together with either the new Cockatiel or the 4 new Budgies, as this will most-likely result in protective, territorial behavior from the two Cockatiels that are already bonded closely and who have been living together in their cage...They will naturally protect each other AND protect their cage, as they are territorial, and it's very likely that you're going to end-up with injured or dead birds if you just put them together in the same cage...
I hope that you have individual cages for the new Cockatiel, and then also for the 4 Budgies (if they were housed together at the pet shop or breeder, and if the cage is large enough for 4 Budgies), and that these cages are separate from the cage that your already bonded-pair of Cockatiels have been living in. Because if you just decided to go out and buy a new Cockatiel and 4 new Budgies and thought you would house them all together right from the moment you brought them home, that's a very dangerous situation that you're putting them in. It takes time for them to get to know each other, and as I already mentioned, regardless of what you want the end result to be, there is no way at all for you to force any of them to get along. They might, they might not, some of them might, some of them might not, and you're going to have to introduce them all slowly, figure out who gets along with who slowly, over time, and house them separately and allow them time together based on who gets along with who. If you don't do this, you're going to end up with injured birds, plucked/abused birds, or even dead birds, along with unwanted eggs/baby birds (and in the case of the 4 Budgies, possibly inbreeding if they are siblings).