The distance from Rockville to the airports (approximately) are as follows:
- DCA - 25 miles
- IAD - 25 miles
- BWI - 50 miles

Transportation options are:
- IAD - No public transport. Rent a car or uber/taxi
- DCA - Metro - served by the Yellow and blue lines. You would have to change to the red line to get to rockville (1 - 1.5 hrs travel time)
- BWI - Bus #201 from BWI to the Shady Grove Metro Station in Rockville. Fare is $5 one way. The bus uses the new Inter-County Corridor. Travel time about 40 minutes.

At 5 PM, I would not recommend BWI as all rush hour commuters are heading home from DC to Baltimore.
IAD - 270 South to the beltway should be OK (the rush is going north). Heavy traffic on the beltway from 270 to the Dulles Access Road. Dulles access road is for airport use only - 2 lanes with little traffic

DCA - Common route on 270 South, beltway west to the GW Parkway South. Goes straight to DCA. GW Parkway may have heavy traffic.

My personal opinion is that IAD might be best for you at 5 pm.