The 5:50 part is related to Orphan and Barthandelus, you can hear the hilarious UP DOWN UP DOWN UP DOWN UP DOWN chorus saying "Via-tor-e-la-men-ta-bi-lis" Each syllable coinciding with the respective UP/DOWN melody. This UP/DOWN melody is heard in Nascent Requiem too (in the piano solo part if I'm right).
BTW I'm getting the feeling the theme itself wasn't composed from zero. The only tune which is original is the "Deum volat cum ira" part, the "Par alientis" and the "Omnidei" (all of them have The Ark as a base tune). The other tunes were extracted from their original themes:
1. The Saber's Edge part. Piano only. 2. I think that the part between Saber's Edge and Caius's Theme is indirectly extracted from the final part of "The Cradle Will Fall" from FF13. 3. If you noticed, "Caius's Theme" does not include the first verses (Dea mortis juravi carissima servaturum). This version is extracted from "Chaotic Guardian" from FF13-2. You can clearly hear the same stuff. 4. The "Fighting Fate" parts are totally copied from the original theme. "Nascent Requiem" has a cameo at 5:50.