You've mentioned that your houses have cribs, but you didn't say if there were enough beds. A homeless family of 5 is going to need a lot with enough beds to sleep 5 sims.
I went in and added extra beds to all available houses in the price range and extra cribs, just to be safe, and getting the same thing. But yeah - these are all 1 person and 3 person families, with more beds and cribs than necessary.