Absolutely no way top 5.
Leaving my own personal mixed feelings aside for a second, consider this:
#1: Legislatively, his biggest accomplishment was the ACA, which has continued to have a really messy history and clearly needs to be fixed. It might end up being a step towards universal health care, but he ain't getting full credit for something that isn't going to get fixed until who knows when.
His second biggest accomplishment was the stimulus bill. Again, sort of mixed. Past that no one remembers anything.
#2: Domestically as an inspirational leader, he doesn't have a big moment. I guess the closest you come are his reactions to Trayvon Martin or Charleston, or maybe killing Osama. But he doesn't have any national disaster or great victory that he led us through.
#3: On foreign policy, he had Afghanistan for 8 years and it's still going, he got out of Iraq and then Isis came and we had to go back. The Iran deal and Paris are his two best moves and Trump looks likely to ruin both of them.
And then on the negative side, you have drones, wiretapping, Libya, removing the filibuster on judicial appointments, some sketchy uses of executive power, and a continuation of the increase in partisan conflict.
Obama is going to go down as a smart, well-informed, even-keeled, well-intentioned president who got dealt a lot of shyt hands and made some mistakes, but generally steered the USA competently through his eight years. And the fact that he was a great speaker and broke the color barrier will be remembered.
In the eyes of the public, I don't think that's enough for him to ever move into the top-5.