WMG (which may have been obvious to some, but I just realized it): five may have had to choose between stopping the apocalypse or saving ben’s life
Of course, the meta reason is that Ben was dead in the source material so he had to stay dead in the show, however in-universe reasons have a lot of angst potential.
Perhaps, the exact date of Ben’s death wasn’t disclosed so it would have been too much of a shot in the dark for Five to try jumping just before it and thus couldn’t factor it into his equations. But why not just try jumping to the exact moment he left? More time to stop the apocalypse right? And he could also save Ben in the process knowing what’s coming. Even if he came back in his actual proper-age body, and his siblings wouldn’t have believed him, he could have worked in the shadows.
But precisely because he knew what was coming, he couldn’t jump to a time where he could have prevented Ben’s death. Because Ben dying was in Vanya’s book. He couldn’t interfere in the events that he knew of from the book because if he did and something changed in the book then something drastic could change in the timeline such as the schedule of when the Apocalypse would happen. That was the only sure thing he knew, the day the apocalypse happened, and he couldn’t risk that certainty. Thus, he only had leeway to move in the events that happened after Vanya’s book in order not to risk changing that timeline drastically and lose his only advantage.
Besides that, if he returned to right before Ben died in his 58-year old body, which was his original plan, there was no guarantee he’d live long enough to the day of the apocalypse.
So no, I don’t think it was the impossibility or convenience of it that stopped Five. Five, the boy then man who spent forty five years perfecting his equations? You mean to tell me he couldn’t find the exact equation to bring him back to the exact moment he left?
And of course it wasn’t a lack of love for Ben. Again, Five who literally turned back time to save his siblings who already died - he literally raised them back to life thrice! Five, who called Ben’s name in the apocalypse right after Vanya’s? You mean to tell me he wouldn’t have done anything in his power to save Ben too, to save his whole family?
And that’s what makes it so heartbreaking, that it wasn’t a cold, easy, and pragmatic decision for him. The life of one compared to the life of billions. It always struck me how personal his line seemed to be in the last episode of s1 - “We’re past the point of trying to save just one person.” What if he was also talking about Ben, as well as Vanya?
Another point of heartbreak is the implication that Vanya and Ben were his favorite siblings, or at least the ones he get along well with the most. He had to let one die to stop the apocalypse, only to find out that the other one was the cause? And that she might have to be killed too if he really intended to stop it?
And Five, Five would say that it was needed, but he would never justify himself or absolve himself of guilt. I don’t think he would have thought, it can’t be helped, it already happened. He had the power to freakin’ time travel. He knew what would happen. He could have stopped it. But he didn’t. I think that was a conscious choice, and a part of Five, buried deeply under the sarcasm and coffee and cold-bloodedness probably thinks he willingly let Ben die, and didn’t do a single thing to stop it.
And I think this also contributes to his obsessive need and compulsion to keep the rest of his siblings alive, come hell or high water. He already failed one of them; he’s not going to fail another one ever again.