It is not possible to drive from Washington DC to the Grand Canyon to Los Angeles to San Francisco and back to Washington DC in 5-7 days. If you took seven full days, this would require that you drive at least 1057 miles per day or ~ 19 hours a day, including traffic delays, fuel stops, rest, sight-seeing, etc.
The absolute minimum number of days we would recommend for this route would be 12! And like AZBuck mentioned above, you would really need three full weeks to drive this route and be able to actually see anything...
You need to re-think some of this.... I would recommend that you do a fly-n-drive. Fly to Phoenix, go the Grand Canyon, over to LA, San Francisco and back to Phoenix. Even this would be pushing it -- but you could probably do most of that route in 5-7 days.
Mark