I think you are rather arriving at 5:50 am (there is no flight arriving from IAD at 5:15). As you have plenty of time, I recommend you to exit 2E (as if you were ending your trip in Paris) and go to 2C to the AF arrival lounge. This is the best place to have a shower in AF lounges at CDG. Then walk to 2D. Allow you about 15 min to reach your gate in 2D as you are entitled to use the fast track lane to clear security. These fast track lanes are called "accès n°1" and in 2D they are mlocated in the middle of the terminal, almost accross the stairs of AF lounge in 2D.