Your play here....

[adanthar]

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It should be pretty obvious that BB has 86 here about 95% of the time.

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That's completely false. I'm willing to admit that BB has 99, 55, or 86 95% of the time.

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FYP; he doesn't have 2 pair. 2 pair would put in the second raise, but not a fourth. OK, MAYBE 97, if you hadn't had sevens instead of fives.

Kyro and KilgoreTrout are both right; the flop play is by far the worst part of the hand and this situation should never happen. But now that it has, your best bet is to get to showdown as cheap as possible. You are way ahead of UTG+1 (who probably has an overpair, A9, etc. - doesn't matter) but most likely way behind the BB with 55 the only hand you beat.

I'd call a decent turn bet (because if the board pairs, you probably take his stack; hope he doesn't have nines) and fold to a push.

Disclaimer: If this is $10 or under you may as well just push yourself because the third guy will call and give you odds to fill up, plus the increased chance BB's a donkey.