In a large enough tank, there is a chance angels and bettas could get along but it's certainly not a guarantee, so you need to have an emergency plan in place in case you realize a few hours after putting them together that this isn't working. You might have more luck with female bettas; I would be pretty worried about a male betta going after the angels because of their large fins. (You know the way men are--they are always out to prove they have the largest...um...fins.)
As as for bettas themselves, under no circumstances can you keep two bettas in a 5 gal
1. If both are male, they will fight to the death, almost certainly within the first 24 hours and quite possibly the first instant they spot the other one.
2. If it is a male and female, it is quite likely the male will kill the female as well, or at the very least harass her mercilessly until the stress from it either directly kills her or indirectly kills her (by making her susceptible to some sort of disease).
3. If it is two females, the dominant female will harass the weaker female, eventually leading to the same result as #2.
Assuming you had a larger tank, you *could* keep at group of 4+ females together. They will bicker amongst themselves for the first week or so and then establish a hierarchy. The dominant female still might pester the others but her aggression (if there is any) will be spread out among all of them, so no one single fish will always be victimized.
Note that this is "usually" the case. Occasionally you'll run into a particularly nasty female who just doesn't tolerate anyone and won't be happy until she has a little tank all to her lonesome. It's rare, but it happens. Bettas are notoriously individual in their personalities--one of the reasons I (and many others) like them so much. But if you end up with a real antisocial one, you need to have a plan in place to get her into a tank by herself--both for her sake and for the sake of your other fish.