He's already on his "adult" diet if he's weaned, which he would be at 5 months for sure. The "baby" diet is simply hand-feeding formula, and they are actually weaned onto their "adult" diet. I agree that whatever brand/type of pellets the breeder is feeding him is what you need to buy at first, and maybe it's fine and you keep feeding it, maybe it's not and you then decide what pellets you want to feed him and you start mixing them into the ones that he's currently eating, and slowly switch him over. If he's currently eating a "Natural" flavored pellet, meaning one that is NOT a "fruit" flavored pellet, then chances are that it's a good pellet and it's fine to keep feeding him...You do not want him to be eating a fruit-flavored pellet, as they are full of sugar, which turns into fat, which causes Fatty Liver Disease, Diabetes, etc. just like a junk-seed diet does. So it's just going to depend on what pellets his breeder weaned him onto, though it's great that he actually weaned him onto pellets in the first place, because it's a lot easier to switch him from a fruit-flavored pellet to a "Natural" pellet than it is switching him from a junk-seed mix to pellets.
There are a lot of great "natural" flavored pellets out there, and it pretty-much comes down to which one your individual bird will like. Like I said, if he's already eating a decent, natural-flavored pellet then you're really lucky and no reason to change anything...The most-commonly fed natural-flavored pellets by experienced parrot owners that provide them a well-rounded, varied, nutritional "staple" diet are Harrison's, Tops, Mazuri, Zupreem Natural, LaFaber Pelletberries, Tropican, among others (those are the most popular, common ones). So if he's currently eating any of those he's in good shape. I'd call his breeder ahead of time to find out; most of these are available at the major pet stores like Petco, only the Harrison's and the Tops are a bit harder to find in stores and are actually much cheaper if you order them online anyway (some smaller, non-chain pet shops and Avian Vet offices do sell Harrison's and Tops as well, but you'll pay a lot more than you will if you order them)...
So the pellets are going to be his regular, daily "staple" diet, meaning the main-component of his diet, and he should have a bowl of pellets available to him all day long, every day so he always has his healthy, "staple" diet available to him, along with fresh, clean water. Now you may or may not want to also feed him a small bowl (I feed 1/4 cup per day) of a healthy, varied, low-fat seed-mix that does not contain ANY sunflower seeds, no nuts/peanuts, and no corn. Some people do, some people don't. I do simply because pellets do not exist in nature, and it's a fact that the anatomy and physiology of a bird is designed to shell, swallow, process, and digest seeds, grains, and legumes, specifically their GI Tract (crop, gizzard, stomach). I also believe that eating seeds on a daily basis is good for the bird psychologically, as it is what they innately eat in the wild. This is a topic of controversy, but usually the source of the controversy comes from the fact that people often choose crappy, junky, high-fat seed mixes and that is the bird's "staple" diet. If you feed a healthy, varied, low-fat seed-mix in a very small quantity each day it actually does benefit the bird physically and mentally, as long as it's only a supplement to the "staple" diet of pellets. There are quite a few very healthy and varied seed-mixes out there, including Tops, Zupreem Sensible Seed, Tropimix, Higgins California Blend, and many others that again contain no sunflower seeds (preferably no safflower seeds either), no nuts of any kind, and no corn. So that's a choice that you have to make.
As far as fresh veggies and dark, leafy greens, he should get a portion of them every single day, and you can basically choose any fresh veggies and dark, leafy greens except for onions and any other veggies in the onion family, such as leeks, as they are toxic to birds. So every other veggie, as long as it's fresh and not ever canned (frozen isn't horrible, but fresh is obviously best) is fine, it's a matter of finding what your individual bird likes...Green Beans, Peas/Pea Pods, all types of Peppers, especially the Bell Peppers, Broccoli, all types of Squash, Okra, Cauliflower, Carrots, Eggplant, basically all veggies besides the Onion family. A "Chop" is a mix of many different fresh veggies, fruits, and/or grains in different combinations that birds just love. There are a ton of great "Chop" recipes in the Food/Diet forum here. I usually feed my guys their fresh veggies/Chop when I'm eating my own dinner, or if it's a day when I'm home all day I feed them veggies/Chop at both lunch and dinner. So they get their natural-pellets first thing in the morning and then have them in their bowl all day long, then I also give them their little 1/4 cup of healthy seed-mix for breakfast, then they get fresh veggies/Chop when I eat my meals, at least once a day, usually twice.
****It's important to note that fresh Fruit should NOT be fed in the same way that fresh Veggies and dark, leafy Greens are, because Fruit is loaded with all kinds of sugar. A lot of people put fresh Veggies and fresh Fruit in the same dietary category, and then they feed their birds lots of fresh Fruit every day too, and this is not good. Again, just like the fruit-flavored pellets, all Fruit is loaded with sugar, and that sugar gets converted into fat that is stored in their liver, and causes Fatty Liver Disease, Diabetes, among other serious health issues. So I don't really consider fresh Fruit a "treat" per se, but I only give them some fresh Fruit with their fresh veggies/Chop at dinner time, but they only get it maybe 2-3 times a week (again, always fresh, never canned)...You can feed most-all fresh Fruit, except for Avocados, which are toxic to birds, and all Citrus Fruits, as Citric Acid enhances their absorption of Iron from their diet, and birds cannot handle much Iron at all, and they will develop a life-threatening condition called "Iron Storage Syndrome". So it's best to avoid all Citrus Fruits, including Oranges, Grapefruit, Lemons, Limes, etc. All other fresh fruit is fine, such as apples, bananas, pears, kiwis, mango, guava, starfruit, passion fruit, strawberries, blueberries, blackberries, raspberries, etc.
As far as "treats" go, this is a broad category and should include both commercially-bought bird treats, AND people-food. Most birds absolutely love Sunflower Seeds, and since you won't be feeding them to him in his regular, daily diet, Sunflower Seeds make a great "training treat", as do all nuts. Sun Conures have a large enough beak to crack some in-shell nuts, such as Almonds, so they also make a great training-treat (cut them into slivers if using them as a "training treat", as these treats need to be able to be eaten quickly). Other nuts such as Brazil Nuts, Filberts, Hazelnuts, Walnuts, Pistachios, etc. are all good occasional treat. Try to avoid feeding him many, if any Peanuts, as they are extremely fatty; if you do feed him the occasional Peanut as a treat, make sure that it is NOT in the shell, as whole-Peanuts in the shell often contain a type of mold that is deadly to birds. Also, most birds love foods such as plain Oatmeal, plain Grits, etc. So on weekends my guys get plain Oatmeal for breakfast instead of their healthy seed-mix. They love it. And of course your bird is going to ALWAYS want whatever you are eating. People-food should be considered a "treat" and be fed in very small quantities. Try not to feed your bird any dairy products, or at least in very small moderation, such as cheese, as they cannot properly digest lactose and it can make them sick. They love cheese, and I give my guys a small bit when I'm eating it, but that's it. And make sure that anything you feed your bird is totally unsalted, and does not have any butter on it!!!