No, no one has 5 rivals, but that's the point.  That's what makes this hard.
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Florida:  FSU, Georgia, and Tennessee, right off the bat.  Those are easy.  Then we have Carolina, basically all because of Spurrier.  It won't last, but it's a thing.  Plus we have Miami historically, and maybe someday they'll get back together.  Auburn used to be a big thing, too.....historically placing 3rd, behind UGA and FSU.  But divisions took care of that one.
No, LSU still isn't a rival.  They never were.  We were thrown together because reasons.
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Historical:  Georgia, FSU, Auburn, Miami, annnnnnd Alabama (mostly bc everyone wanted to beat Alabama)
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Modern:  FSU, UGA, Tennessee, Carolina, Miami (rarely play, but it's a huge deal when we do)