I have a 30 year fixed FHA loan at 5%. What would be a good rate to refinance so my monthly payments

The answer depends on when you took out your existing loan. FHA doubled their mortgage insurance premiums last April, effectively preventing many FHA borrowers from refinancing. For instance, if your monthly MIP is now $50, it could end up at $105 or so when you streamline (unless you took the loan out after April and are already paying the higher MIP). If your MIP is doubling, you have to lower your rate by at least 1 1/8% to meet FHA’s savings requirements. Keep in mind you also cannot roll any closing costs into the loan unless you do an appraisal to document value. Bottom line is you likely need 3.75% to 3.875% to make this work, which may not be as far fetched as it sounds. Always be sure to account for the closing costs incurred, and remember that FHA will also roll a 1% upfront MIP fee into your loan. You might get a partial credit from your existing MIP if the loan is less than 3 years old, so that can help offset the cost of the new MIP.