The usual rule of thumb is that you should start considering refinance when you can lower the effective interest rate by 1% or more. If you're now paying 4.7% this would mean you should be looking for loans at 3.7% or better to find something that's really worth considering.
One exception is if the bank is willing to do an "in-place refinance", with no closing costs and no points. Sometimes banks will offer this as a way of retaining customers who would otherwise be tempted to refinance elsewhere. You should still shop around before accepting this kind of offer, to make sure it really is your best option.
Most banks offer calculators on their websites that will let you compare your current mortgage to a hypothetical new one. Feed the numbers in, and it can tell you what the difference in payment size will be, how long you need to keep the house before the savings have paid for the closing costs, and what the actual savings will be if you sell the house in any given year (or total savings if you don't sell until after the mortgage is paid off).
Remember that In addition to closing costs there are amortization effects. In the early stages of a standard mortgage your money is mostly paying interest; the amount paying down the principal increases over the life of the loan. That's another of the reasons you need to run the calculator; refinancing resets that clock.