Need to get to my computer... too long for phone typing...
OK, this is one of the great mysteries of the awakening. And depending on where you look, you will get a different answer.
First, knowledge of the "Immortals" is more an open secret than common knowledge. And those that are known to be immortal, are not talking. Or, if they
are talking, they contradict themselves.
Also, different things seem to have happened to different groups.
DRAGONS:
The only dragon that we
know cam from a Rift, is Ghostwalker. Several thousand people watched him force his way through an Astral Rift to confirm that... As well as the hordes of Shedim that accompanied him... (Make of that what you will)
As for the other Dragons, well, Ryumo(SP) was seen emerging from an erupting MT Fuji... so yea maybe rift? Maybe naptime at the bottom of the volcano? Big D was said to have emerged near Lake Louise, and did claim that area as his person lair and property before moving to an island.
However, there is evidence that All, some, or at least the Big D was awake during the 5th age for at least brief periods of time. This is from some interviews given early in the fluff, and novels of the 2e books. Also, there are the gifts in his Will.
Add to that deeds, stocks, bonds, accounts and titles the dragons pulled out of their ass (and used to set up their little empires... Looking at you Lofywr(sp) )... How they got those things is anyone's guess... Did they walk around spending coins to acquire these things? Use intermediaries? Hell, just possess some sod mind with Dragon magic? No one knows for sure.
Keep in mind too, there is only handful of Great Dragons... but hundreds of Dragons... (down from a few thousand after that little dragon dust up a few years back), and the power gap between a dragon, and a Great Dragon is well, GREAT.
Immortal Elves.
Yea, these jerks have answered this question with 10 different answers over the years... Which one is the truth? No one knows... but the most common theme is that the Immortal Elves where awake, and living as basically immortal
humans, during the 5th age. Some claim that during the 5th age, they lives dozens of "human" lives, but retained their same personality and knowledge during each birth.
Surehand claimed to have spent the entire 5th age as an elf, hiding his "Elfness" from humans using mundane means. One even claimed to have been a part of a cabal of immortal elves that hunted dragons during the 5th age to kill them off, and managed to get a few of them!
So, yea, take your pick which true. Because the Immortals aren't saying.
Vampires.
Its believed HMHVV was dormant during all of the 5th age, and only emerged again with the awakening and the rising mana levels. However, there has been a few vampire that have claimed to have been around in the fourth age, or made in the 5th age. But those ones are currently dead, thanks to one of their kin, so for sure answers are hard to come by.
Fey:
These bastards didn't show up until years after the awakening, and most fo them through Rifts so they were most likely trapped there until mana levels rose to a level that could support an Astral Rift. And considering we can't keep them here when dead, suggests they are not native to the material plane to start with.... But actual facts? None. Sorry.
Which all boils down to:
What ever you want for your table, go with it