Flying Ants or Termites?

I have woke up the the past two mornings and found swarms of flying ants and little red ants in both of my bathroooms. I have looked on the internet about the differnces between termites and ants. Unfortunately any crawling creature makes me nervous so after they had been dead for a while a put them in a plastic bag and examined them. They do seem to have 3 body parts, a bent antennae, and no beads on them. (I couldnt bear to tear the wings off of them )They appear with tiny red ants on the floor. I live in a slab house and we just had a termite inspection 5 years ago when we moved in. My husband says not to worry because they are ants but i am so afraid they are termites.. Please any information would be greatly appreciated.