Originally Posted by choster

There's plenty of time to take Metro. The 5A bus to Blue Line train involves the fewest transfers; on Sundays there's one bus an hour leaving on the :40s, and the schedule is reliable. Departing IAD curb 2E at 4:42pm, you should at Rosslyn around 5:16pm; from there you can take the Blue Line train to DCA, which takes about ten minutes. Cash fare is $4.45.

If you clear customs and immigration earlier, you could take the Washington Flyer coach to the West Falls Church Metro Station; it bus departs from the main terminal building on the :15s and :45s. It's a cleaner and more comfortable coach than the Metrobus, with a place to stow your luggage, but you'll need to make an extra rail transfer, from the Orange Line to the Blue Line at Rosslyn; the ride from West Falls Church to Rosslyn is about 15-20 minutes and from Rosslyn to Reagan is another 10 minutes. Total fare would be $9 for the bus plus $1.85 for the train.