| Any quest involving Scar is part of the main quest prior to chapter 5, but feel free to do them until after visiting the Iron Throne HQ. Going back to the Flaming Fist HQ after that triggers the move to the next chapter, the invite comes later than that. There are two (at least) very good reasons for continuing with the main quest beyond that point. I'd suggest continuing the MQ, as well as side quests, until shortly after meeting some basilisks.
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