I wouldn't ever fold in this scenario at 5.50. I would push. He's not folding and I believe he has an ace but you have him outkicked.

I'd guess 10-20% you're beat 80-90% you have the best hand.
(With a very good shot it's 0-100 in your favor)
Can't believe someone at that level would be that capable of not pushing with a full house at any point in that hand.