Hi,
Beijing offers lots of must-sees. What you should not miss during your five days stay are Tiananmen Square, Forbidden City, Shichahai, Badaling Great Wall, Altar of Heaven, Summer Palace, Old Summer Palace, Fragrant Hill and say, Peking Universtiy since you six are all students.
For low-priced hotel, you can check out youth hostels in Beijing, such as City Central Youth Hostel (Chengshi Qingnian Jiudian), Gongti Youth Hostel (Gongti Qingnian Lushe), and Far East Youth Hostel (Yuan Dong Qingnian Lushe).
Wish you a good time :)