Sadly, it looks like never for both shows. But I can only say "looks like" because you can never count Jeff Foxworthy out.
Foxworthy, who hosted both shows, has already given us an unlikely revival of "5th Grader" in 2015 (not to mention a number of "revivals" of his Blue Collar Comedy franchise). However, neither "5th Grader" nor "Bible Challenge" has produced a new episode in years, which is generally a bad sign.
"The American Bible Challenge" aired for three seasons on the Game Show Network, from 2012 to 2014, and hasn't been heard from since. The series featured Foxworthy testing contestants on their Bible knowledge.
"5th Grader" had a higher profile than "Bible Challenge," airing on the Fox broadcast network rather than on cable, and it also lasted longer. It debuted in 2007 and was first canceled in 2011. It was revived in 2015, but failed to do any better in the ratings, and so was dropped from the schedule again.
So it seems likely we've seen the last of both shows, though not of Foxworthy. He's been busy already, having released a comedy special on Netflix last year ("Jeff Foxworthy & Larry the Cable Guy: We've Been Thinking") and voiced a rather famous ox in the animated feature film "Bunyan and Babe," about the legendary woodsman Paul Bunyan and his blue ox, Babe.
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