Refinancing isn't just about capturing interest savings. By extending the term of your mortgage, especially if you can get a lower interest rate, you can reduce your monthly payment. That can help you live within your means and not run up credit card balances to finance current expenses.
If you were going to be in the home for 30 years, you could wind up paying more in total interest expense on the refinancing versus staying in the current loan. However, you don't have a 30-year horizon, so you'll be out of the mortgage when you sell your home.
If you have enough equity in your home, you can tap that equity to pay for the closing costs. Basically, that means rolling the closing costs into the loan balance. If closing costs are $4,000, you'd borrow $102,000 when you refinance. Alternately, the lender could bake the closing costs into the interest rate on the loan.
There are costs other than closing costs that need to be paid when you close on a refinancing. One of the big ones is per diem interest. That's the interest expense on the loan from closing to the first day the next month.
You stated your goal, and it isn't to capture interest savings. That said, with good credit and a solid equity position in your home, you should be able to reduce the interest rate on your mortgage by enough to recoup the closing costs over your five-year horizon.