Google is such a wonderful resource, though the reddit thread where I'm getting my info is a year old and it's too late at night (past 2 am) to dig deeper... Apparently, it's not on ANY streaming services. Netflix will send you the DVDs of each season (I don't know if that's an option for you, but you did mention them). The next best suggestion was to purchase the season DVDs on Amazon for $15 individually (because, oddly enough, the full series of 5 seasons box set costs twice as much, $120, than buying them this way). For digital downloads, iTunes has the seasons for $16 each, and Amazon has them for $30. There are also movies, but the reddit thing didn't have their costs.
There was, also, this little gem...
Here is an Amazon reviewer's suggested viewing order of the series and additional movies:
1. Watch the B5 movie "The Gathering" The Babylon 5 pilot movie The Gathering was originally broadcast in 1993 a full year ahead of the regular show.
2. Season 1
3. Season 2
4. Season 3
5. Watch Season 4 up to episode "The illusion of truth"
6. Watch the B5 movie "Thirdspace"
7. Season 4: continue with episodes 9-22
8. Watch Season 5 through to and including episode "Objects at Rest"
9. Watch the B5 movie "River of Souls"
10. Watch the B5 movie "In the Beginning" This is a prelude set 10 years before Babylon 5. Against the logic of the title, I would strongly recommend seeing it at this stage. Should one see it before Season 1, much of the suspense in the main series would be ruined.
11. Watch the B5 movie "A Call to Arms" This movie lays the groundwork for the spin-off TV series "Crusade".
12. Watch the B5 movie "The Lost Tales" [Thanks to Eric Pregosin for his comments to build on the original list]
13. Watch the B5 movie "The Legend of the Rangers" [Thanks to Lisa for her recommendation]
14. Watch Crusade Series
15. Season 5: watch final episode "Sleeping in light"