To Zhongshan with 5 day entry to Shenzhen?

Hi, I wanna go from Hong Kong to Zhongshan to visit a friend. Since I don't have time to apply for a visa in Hong Kong, I thought of going with this option: 5 day entry for the Shenzhen area. I tried to find out if Zhongshan still belongs to the area but could not find any information on that. Does anyone know whether I am allowed to go to Zhongshan with this type of permit? Thanks.