I noticed this discrepancy too, and just kinda put it down to inconsistent writing, but after reading your question I decided to rewatch the episode to doublecheck if there is anything there that might explain this, and I think I now realise the difference.
In all the previous time jumps Five took, he effectively ripped a 'hole' in spacetime and travelled through it, like opening a door and stepping through into another reality. This method of time travel also clearly changes the timeline itself (whether the original timeline still somehow exists somewhere/when as well, or is rewritten, is not shown, and irrelevant to the show as we, the viewers, experience it).
This is evidenced by the reality at the beginning of season 2 being moments before the beginning of WWIII, something that did not happen in the original timeline shown in season 1. Also, we saw the moon rip apart at the end of season 1, but we know this was not part of the original armageddon as it was still clearly in the sky when oldFive was wandering the wastelands for 45 years after armaggedon. The existence of both young- and oldFive in the same timeline fits with this as well - Five is quite literally ripping a hole in the fabric of reality and entering through it, and can even meet other versions of himself in the new timeline.
However, during season 2 episode 6, Five had a quite revealing talk with his father, where he discussed his time travel abilities and the problems he has with it. His father suggests he needs to take baby steps:
Start small. Seconds, not decades.
We have already seen that the children are still learning about their powers, and they are growing and maturing through use. Vanya is the obvious example of this, but we see it with Klaus as well, from just being able to see and hear the dead, he develops his powers to enable the dead to interact with the living world (Ben in particular). I believe what we see in the final episode of season 2 is Five learning a new trick, so to speak.
As he lies there dying, he remembers his father's words about seconds, not decades, and when he uses his power this time, it is shown on screen to be very different. This time, he didn't rip a hole in spacetime and travel through it. We actually see the other characters moving in reverse, as time itself is reversed. Five has taken his powers to a new level.
What I suspect is happening here is that Five is jumping back a only split second and reinhabiting his existing body each time, repeating this exercise multiple times until he has reached his goal.
He has effectively moved on from jumping himself through time to actually reversing time itself.