Wow, that is not a trip I would want to take. I fly on points all the time, too, so I am no stranger to having horrible connections offered to me by airlines, but I would not have accepted this even if it cost me nothing, I would have found some other way to get there. But, I get it, sometimes you just gotta do what you gotta do, so onward.
Can't help you much with the best choices to get from IAD to DCA, but I'd expect that with over 5 hours to play with, you should be able to make it. Hopefully your inbound flight will be on time. Just take into account that you will probably not be at your sharpest after the long flight from Frankfurt, so plan accordingly. It won't exactly be fun after the long inbound flight, but you should make it. Just be careful.
Actually, I'd be more worried about missing the connection in Chicago than in DC. Personally, I find ORD to be a chaotic and challenging place to connect. 1 hour 14 minutes is a tight connection for ORD IMHO. Hopefully you won't have to change terminals (or drag a lot of bags). Presumably, this is all on United (it's exactly the kind of "bargain" business class option they love to offer), hopefully all on one ticket. If this is all on one ticket, then they'll get you to your destination eventually. If this is not on a single ticket, and/or if you have to change terminals in ORD with a bunch of luggage, you better be on your toes there in Chicago (which is probably a big ask after what you will have been through in the previous 24 hours).
Where does your onward flight from ORD take you? Hopefully not someplace too far away (and with no additional connections...). In any case, does not sound like my idea of fun (and I put up with a lot of fight choices that many here would avoid).
Good luck.