Financial advice/debt consolidation/refinancing ?

my husband & i have about 5000 dollars in credit card debt. he is the only one working im unable to find a job that suites the hours im able to work. well we purchased a house in may & walked into it with about 80,000 dollars in equity we currently have a 5.74 interest rate. were considering refinancing but were not sure if its to soon to do. we would take out more than 5000 if we refinanced maybe around 10,000 to do some much needed updates to the house. if we don't refinance does debt consolidation hurt your credit? my credit is trash right now because i put my credit cards off to keep his up due to his job being strict on credit issues. i bring in 320 dollars under the table doing yardwork. any advice or options? i just mainly want the credit cards done it would be such a relief! thanks in advanced! last we checked my husbands credit score was around 600 between 624-650