Travel time to Downtown Frankfurt/taxi or Mainz/S8 Train will be about the same (give yourself 1 hour each way). I've experienced taxi rides to the downtown of almost an hour and I've also had a nervewrecking 30min+ delay on the airport bound S8 once as well.

But a five hour (8:20 a.m. to 1:40 p.m.) lay over is realy not much.

Considering you probably will not get out of the airport till 9AM at the earliest, assuming no inbound delay, and will have to be back by Noon at the latest, this doesn't give you more than an hour for any sight seeing. This may not be a good idea with small children.

Your best bet is to relax in the old terminal's central cafe area for an hour or two.