Aight. Just warning you, very used to Advanced reviewing, so I may end up being too harsh.
*cries when he realizes he can't search Egyptian Gods with this*
Well, let's talk about the reversal itself first. LP gain itself is slightly weaker than LP loss, especially in this regard. You're removing your BP from the picture, meaning for now, there's no real threat to your OTKing tactics and the like. The thing about Brethren and its LP loss is, coupled with BP prevention, you gave your opponent more of a chance to kill you with your Normal Summoned monster in ATK position. Now, you're giving your opponent slightly more staying power...which they don't really need, considering you have a clear field. But you can't Normal Summon, you may respond. This is true. But plenty of Level 5 or higher monsters can SS themselves from the hand.
Secondly, the actual searching. Although the gap from 5 to 12 is much larger than the gap from 1 to 4, you're going to be running mostly Level 4s or lower in a Deck (with quite a few exceptions, actually, but still relatively few), so that shift is fine. What's not fine is the freedom them given. Brethren ties your monsters to the same as the Summoned monster, but with so many Type/Attribute Combos open to you, it's not really that much of a restriction when it comes to monsters having any number of Levels from 5 to 12. Let's take an archetype like Jack Knights, for instance. You have Level 5s to Level 8s, and no real reason to Normal Summon, so they would love to have a card like this in their midst. Then we have Chaos/Lightsworn and even most Pendulum Decks (Qliphort? They have 3 different Levels for their monsters). It can be an easy way for them to search, going +1 for very little.
My suggestion? Attribute nerfing. I can't think of any Attribute varying Decks with a lot of high Level of monsters (Qliphort: EARTH, Chaos/Lightsworn: DARK and LIGHT (not 3, so still not enough for the card), Pendulum Magicians: mostly DARK, Jack Knights: LIGHT, etc.). Perhaps buff the LP gain for your opponent...but it might still be fine.
Your opponent gains 2000 LP, then reveal 1 Level 5 or higher monster in your hand; during the turn you activate this effect you cannot Normal Summon, also add 2 Level 5 or higher monsters from your Deck to your hand, whose Level, Attribute and name are different to each other's and the revealed monster's. You cannot conduct your Battle Phase during the turn you activate this card. You can only activate 1 "Connections of the Emperors" per turn.
Oops, forgot that last HOPT was needed on this card. Brethren prevents from SSing, meaning you can't activate it again even without HOPT, but not so this card.
Still, like the idea, and the implementation. Just a bit too free :3