Yeah, First Contact takes place during season 5 of DS9. I remember well seeing the movie in the theatre at the same time the show was being broadcast--it was the first year I was really getting into Star Trek. Episodes from earlier seasons I had to catch in re-runs and there are still a good number I've never seen. As soon as I finish Chuck season 3, Deep Space Nine is going on my list and this time I'm going to start from the beginning and watch the entire series. I love the show more than I can say, though I go long periods of time without thinking about it. It might be my favourite of all the Star Trek series, though Next Generation is awesome too.
Actually, I kind of wish they had done more to connect DS9 with First Contact. There could have been a scene where the decision to send the Defiant with Worf in command was made, and more discussion of what effects the Borg attack had on the Federation's strategic capabilities. There is a passing mention of this at one point (In Purgatory's Shadow, I think), but it could have been more involved. And given that the Defiant was heavily damaged in the film (didn't seem to do so well considering that fighting the Borg is what it was originally designed for!), it being out of commission for repairs could have been a plot point, as in 'Gee, sure wish our kickass ship were around so we could foil this evil plot over there!'
Ah well. I seriously love the Defiant, it's so cool to see them have a ship that just blows away everything else and has a cloaking device. About damn time the Federation got to play on those terms . . .