Let me get this straight - you owe 5 grand on your credit card, so you're looking to take out an unsecured loan to pay off that debt outright at a lower rate of interest?
If so, I think you're definitely on the right track - the fact that you're paying off your credit card in full should be helpful to your credit rating, but more importantly, the fact that the loan repayment rate is lower should definitely help control the debt and make it easier to control.
Just ensure the card is fully paid, then consider destroying it - when someone feels their debt is coming under control, it's far too easy to feel complacent and start using your card again - compounding the debt issue.
If you're looking for sources of loans, Northern Rock and Alliance & Leicester apparently have some good unsecured loan rates, though I'm not sure if Northern Rock is in a position to lend at present.
Anyway, best of luck with it.