Do you think that will see a team up between Supergirl and Batwoman in season 5.

Possibly. The writers seemed keen on trying to establish a rapport between them in Elseworlds.

I think it depends on how big the Crisis event is--the impact to the various shows during the lead up and the fallout from the conclusion.

Crossovers are fun, but too much can take away from the individual productions.

Personally, I can't say that I am overly excited by the prospect. Maybe after I get to know the Batwoman character a bit.

EDIT: I think the odds went up with Sunday being Batwoman/Supergirl night. They could create some synergy with a single girl power night event. BW at least pairs better with SG than Charmed did.

I am leaning more towards a season 6 crossover between the two--letting Batwoman get it's feet under itself first, maybe? And, sounds like Crisis is going to be a bigger, longer deal.

If they team-up in Supergirl's season 5, it's likely going to be related to the Crisis.

Like some others, I think it's actually unlikely for this season, outside of the crossover. None of the other shows which have shared nights have had crossovers (unless I'm forgetting and Flash/Arrow shared a night when the pre-Legends crossover happened). Also, at the moment, they're in different universes... unless they do Earth-38 Batwoman, which would be intriguing since Kara hasn't met her yet.

most definitely. they seem almost desperate to have Batwoman ride Supergirl's coattails. They will push it as girl power regardless of how many capable, enjoyable and well acted characters there are already on Supergirl

I agree with others that it is unlikely this season. And frankly it is fine with me if it never happens at all (although I'm sure it will at some point). I've just never been a fan of the whole Bat genre. Too dark for my taste.