The only supplements that are even close to necessary are whey protein and creatine. From what I have read, tribulus doesn’t actually increase testosterone, it increases luteinizing hormone. LH affects sex drive and test increases LH, but it doesn’t work the other way around so you might be wasting your time unless you have issues there.
I’m not sure what you mean by burnouts, but they definitely don’t sound like a good idea if you want to get stronger. You don’t need to ever go to failure to get stronger, and burning out in one form or another is not useful. 5x5 programs are usually good for beginners, but you are at more of an intermediate level so I wouldn’t recommend that, although there is nothing wrong with a 5x5 set/rep scheme per se.
What you should do from this point on depends largely on what you have been doing so far, you don’t want a drastic increase in volume that you can’t recover from and there is no sense in doing a low volume program if you can handle more. I’m sure someone on this forum will recommend 5/3/1, it’s a decent choice but choose a version where you squat and bench at least twice a week. Otherwise, the sample programs on the Sheiko site (sheiko-program.ru) should be appropriate. If you check out The Strength Athlete they have a decent sample program as well.
Whether you prefer full body or an upper/lower split is basically up to you, just choose something that looks good to you and do it.