Hi, we have 5 people who like to travel in Beijing, kindly suggest and budget our 5 days 4 nights trip, thank you.

Hi, you can arrange your plan like this:
D1: Tiananmen Square and surroundings as well as Forbidden City
D2: Temple of Heaven and Summer Palace
D3: Badaling Great Wall or Mutianyu Great Wall and National Center for Performance Arts
D4: Ming Tombs and Sacred Road/Way
D5: Hutongs and Courtyards as well as Birds Nest and Water Cube

the local pedestrians such as Wangfujing and Qianmen can also be visited at night. There you can taste local snacks and go shopping. If you are interested, you can also watch a Kungfu Show during your stay.

As this is a relative long trip, you'd better ask a travel agency to arrange all for you.
All for your reference!