Itinerary for attractions and shopping in Beijing

Here is my suggestion for your itinerary:
Day1: Tian’anmen Square, Forbidden City, Prince Gong's Mansion, and Wangfujing pedestrian.
Day 2: Badaling Great Wall, Ming Tombs, Bird Nest and Water Cube (seeing from outside)
Day 3: Temple of Heaven, Tsinghua University, Summer Place, .
Day 4: Beihai Park and Hutongs for fun, Qianmen and Dazhalan for shopping
Day 5: Art Zone 789 and then Silk Street for shopping
Just for your reference~

To avoid missing any must-see spots in your five days, you are suggested to join a tour. I had ever booked a trip Travel China Guide, a very trustworthy travel agency. You may also turn to them! I remember email address is tourstravelchinaguide.com

May help!