Razz - paired cards

[*TT*]

Lets assume that the villain has precisely a 3-card bike hand (three unduplicated cards 5 or lower) on third street. On 4th street the villain catches a 5. What is the probability that the 5 paired the villain assuming that there are 12 bike cards unaccounted for remaining in the deck including the three remaining 5's? Please include the formula, that would help me bunches because I think i calculated this incorrectly. Thanks in advance!