I play the Draconic Domination Pre-con. commander deck and I edited it, putting cards in and out. Doing so, I put Sunbird's Invocation in the deck. (Whenever you cast a spell from your hand, reveal the top X cards of your library, where X is that spell's converted mana cost. You may cast a card revealed this way with converted mana cost X or less without paying its mana cost. Put the rest on the bottom of your library in a random order.) The deck has a lot of cards that say "Dragons cost 1 less to cast. For example, The Ur-Dragon's Eminence ability causes Crosis, The Purger to cost one less to cast. Making his mana cost 5 instead of 6. Would this trigger Sunbird's Invocation where X is 5 or 6?
Sunbird's Invocation's ability will trigger whenever you cast any spell from your hand, regardless of its mana value or what you paid to cast that spell (C.R. 603.2). It's when that ability resolves that you determine that spell's mana value (and, therefore, what X is) (C.R. 608.2h). (Note that cost reductions, such as that of The Ur-Dragon, don't affect a spell's mana cost or, by extension, its mana value [C.R. 202.3; under C.R. 601.2f, such an effect changes a spell's total cost, not its mana cost].)
EDIT (Jan. 12, 2019): Remove apparently broken link.
EDIT (Nov. 6, 2021): Edited, including to correct rule citations and use recent terminology.
Crosis' converted mana cost is 6.
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EDIT (Jan. 12, 2019): Remove apparently broken link.
EDIT (Nov. 6, 2021): Edited, including to correct rule citations and use recent terminology.