You check it with the hotel concierge? Unless you really don't want to go back to the hotel for some reason.
Also, I'm unsure why you want to leave at 4:30 to catch a 7:40 flight. 5:30 or even 6 seems like more than enough time--it should take about 15 minutes to cab to DCA or 30 minutes to metro, assuming you're not planning on leaving the central DC area.