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I would let the $5k you've paid down post to your credit report and see what it does to your scores.
Might also see what other kind of improvements you can make to your score before applying. If you have small balances reporting on some cards, paying those to $0 could be a big boost. If you have any cards reporting maxed out (over 89% util) paying those down could be good for a lot of points as well.
627 score, 75% revolving util, id say its a no. How much actual debt are you carrying vs your yearly gross income? If its over 30 percent its a definite no.
Whats owed in total still?
Is that before or after the 5000 you paid.