I am glad that you are planning to spend five weeks in China because it is a huge and beautiful country and, even in that time, you will barely scratch its surface.
One word of advice: do read-up on its long history (and know its most important Dynasties) before you go because you will go there with greater understanding and absorb much more as a result.
We spent six weeks in China: travelling by ourselves (not with a "Group") from east to west and from north to south; stayed, as often as possible, in small locally-owned hotels; ate wonderful meals all over China; and saw and photographed many precious treasures. We left there with the strongest desire to return.
Have a wonderful trip!