We have a small mtg. we took out to put an addition on. It’s about 40,000 and the rate is close to 5.1 for a 15 year. I happened to be talking to my bank yesterday and asked if they thought rates were going to go low enough for it to be worth it to refinance. She quoted me a rate similar to yours, but with no closing costs. They are a reputable 5 star bank, so you might want to take a look at their rates: http://www.thirdfederal.com/. BTW, she said, wait, we might see rates even lower.
Make sure there are no fees bundled in. My guess is you could get lower but with no fees they are giving you 4.875%. Make sure there are no doc stamps with your county or recording fees.
$40,000 at 5.1% is almost not worth it unless you can get maybe around 4.375% with no fees. Her advice to wait is probably good.
To the original poster - 4.875% in the current environment is not a great deal on a 30 year. I refied about $150,000 4 years ago or so at 4.75% on a 15 year.