That IS a problem. Unless you can prove physical abuse and have him physically removed, there's not much you can do to get him out of there.
Apartments are almost impossible to find with 5 kids! And they wouldn't be large enough anyway. And besides, most landlords don't want kids in their apartments. Can you afford to rent a house? That would be ideal. I'm sure you could find a moderate sized house to rent. If he could afford to pay your rent along with child support, that would be great!
May I ask why you want the divorce? Is he abusive to you? Does he abuse the kids? Is he a workaholic?
Will marriage counseling not work or have you already tried it? It would be a tragedy to break this marriage up with 5 kids being hurt. Kids are ALWAYS the ones who get hurt in a divorce. It always happens.
I hope whatever happens works out for the best. God bless and take care. Hugs, Lee