Anything I'm doing wrong in the calculation here?
This is just for the flop call obviously, which it appears that you did not have odds - on the turn, you bet, so it's fine then - even if the bet to you was $5 you're good.

10 outs (4 Ts, 4 5s, 2 7s) / Bet: $5 / Pot: $13

21.3% chance to turn an out

To justify calling $5:
the pot must be $18.5

For a pot of $13:
the max you can call is $3.51