The problem with 5.d3 is that Black can develop the bishop to this active square.
1. e2e4  1... e7e5  2. g1f3  2... b8c6  3. f1b5  3... a7a6  4. b5a4  4... g8f6  5. d2d3 Carlsen has plenty of experience with this flexible move that avoids the Open Variation (where Black takes the e4-pawn).