Looks to me like the contact binary may be the likeliest to have a conducive habitable system. The other three stars are far enough that there's room even for planets beyond the snow line. The detached binary stars are still quite close to each other, so plenty of planets could form around them; however, it's not clear where the fifth star is, and whether that would interfere with their planets. Maybe they haven't placed its orbit yet? In any case, the article doesn't give its parameters.
Granted, if the binaries used to be farther apart, and have spiraled in, there might have been less room for planets when they formed.
The source article also notes that the system may have formed about 9 to 10 billion years ago, which would make them pretty old. They might not have had enough material for really big planets. Those they did have, at least, would be less likely to have substantial metals and overall likely to be less dense. Combined with their age, that'd mean they might be likelier to have tectonically dead worlds.
Edit: Fantastic picture! Very evocative.
Granted, if the binaries used to be farther apart, and have spiraled in, there might have been less room for planets when they formed.
The source article also notes that the system may have formed about 9 to 10 billion years ago, which would make them pretty old. They might not have had enough material for really big planets. Those they did have, at least, would be less likely to have substantial metals and overall likely to be less dense. Combined with their age, that'd mean they might be likelier to have tectonically dead worlds.
Edit: Fantastic picture! Very evocative.