Based on Ornamental Weapon:
Ceremonial Blade 1
Artifact- Equipment U
Equipped creature gets +1/+0 and menace.
Whenever equipped creature deals combat damage to a creature, sacrifice Ceremonial Blade.
Equip 1
You need to specify where in the library the cards are exiled from, and the last effect has to be worded in a very particular way for the rules to actually parse it. I think the proper templating for this card (cleaning up a few other things as well) would be:
"You may spend only blue, black and/or red mana to pay X. If X is 5 or greater, this spell can't be countered.
Target player exiles a card from their hand. If they can't, exile the top card of their library. Repeat this process X-1 times. Then, they exile the top X cards of their library. Life-Breaking Binge deals X damage to them. This damage can't be prevented."
You don't need the "without paying its mana cost" when you're just slamming things onto the battlefield; you only need that if the cards are actually being cast, which in this case they're not.
A couple other suggestions that aren't about whether the card works under the rules, so feel free to take or leave them:
1. Wizards hasn't printed a land with no mana ability in quite some time, because people tend to play them wrong, for example, they'll just count the number of lands they have to determine how big they can make an X spell, etc. and forget that one doesn't produce mana. It also makes it harder for opponents sitting across the table to figure out how much mana you have potentially available. That's why most nonbasics at least have "Tap: add C."
2. The last ability is extremely powerful in any environment with artifacts that have CMC 0. I suggest adding the rider "X can't be zero" so that players have to actually use some counters to use the card.