At first, I thought 5 days wouldn't be enough to see Beijing and the Great Wall of China. And it wasn't. Nevertheless, I wouldn't recommend to stay much longer. Certainly, the city hosts some beautiful places of historical interest, which you should not miss out on. But personally, because of the overload of people and the lack of space and air, I experienced Beijing as a suffocating place. Although I still had a day available to go to some temples I had orginally planned on visiting, I preferred spending it inside in a spacious and airconditioned shopping mall. The amount of Beijing I could take in had been reached.
Anyways, I'll share my itinerary with you. I've was in Beijing for five days, but I've only spent 4 days really exploring its sights.
Day one: chill afternoon in the park
Day two: The Forbidden City and its surroundings
Day Three: Day trip to the Summer Palace
Day Four: Walk the Great Wall of China
Day Five: Search for coolness
On this last day I could've gone to so many other places such as the Lama Temple, the Bejing Zoo, the National Museum, the Peking University... It is very unlike me not to visit as much as possible, but Beijing had exhausted me. For once, I was truly happy to skip those places and wander around in all kind of shops - providing it was cool inside.