a group of 8 persons plan to visit Zhangjiajie in end of May,

It will be very warm in the end of May there, but the temperature varies much between day and night. Travelling there at that time, you can wear shorts during the day, but need to wear light jacket at night. It is the peak time for sightseeing.

what about 1st week of july compare with may?

During the first week of July, it will be very hot. The temperature will range from 25C to 36C. If you go there at that time, you need to take along summer clothes. Besides, a light coat is also needed to keep warm at cool nigh, because the temp would drop a lot at night.

Comparatively, July would be more crowded than end of May.