Do the Sufism believe in the five pillars of faith?

Yes, indeed Sufi's do believe in the 5 pillars of Islam. Otherwise, if they did not believe in the 5 pillars, they will not be considered Muslim at all. Like for example; Ahmadiyya Islam. Which they do not believe that Prophet Muhammad (PBUH) was the last prophet. However, some rules of Sufi's do go against some rules of Islam.