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In your hand:

In your hand, Turn // Burn has a converted mana cost of 5 (3+2).
Previously, its CMC in your hand was 3 and 2, but not 5.

If you are targeted by Inquisition of Kozilek, your opponent now can’t choose Turn // Burn for you to discard because its CMC isn’t 3 or less.

In your graveyard:

In your graveyard, Turn // Burn has a converted mana cost of 5.
Previously, its CMC in your graveyard was 3 and 2, but not 5.

Goblin Dark-Dwellers’ trigger can’t target a Turn // Burn in your graveyard because its CMC isn’t 3 or less. 

In your library:

In your library, Turn // Burn has a converted mana cost of 5.
Previously, its CMC in your library was 3 and 2, but not 5.

If you reveal Turn // Burn for your Counterbalance trigger, Counterbalance’s trigger will counter the spell that triggered it if that spell’s CMC is 5. (e.g. Force of Will) It won’t counter a spell with CMC of 2 or 3 when Turn // Burn is revealed.

In exile:

In exile, Turn // Burn has a converted mana cost of 5.
Previously, its CMC in exile was 3 and 2, but not 5.

If your opponent exiled Turn // Burn with their Thought Prison, Thought Prison will trigger when a player casts a spell with CMC 5, not CMC 2 or 3.

One half on the stack:

On the stack, Burn has a converted mana cost of 2. This is unchanged from the previous rules.

When you cast Burn, Chalice of the Void will trigger and counter the spell if there are two counters on Chalice of the Void because Burn’s CMC is 2.

Fused on the stack:

On the stack, a fused Turn // Burn has a converted mana cost of 5. This is unchanged from the previous rules.

Disdainful Stroke can target a fused Turn // Burn that’s on the stack because its mana cost is 4 or greater.