On the one hand, there are a number of references in contemporary sources to Henry VIII's interest in Mary Boleyn. In 1527, the Venetian ambassador wrote that Henry "has lately taken another mistress in place of her sister, a daughter of the Earl of Wiltshire." This suggests that Henry may have had a sexual relationship with Mary at this time. In addition, there are several paintings and drawings of Mary Boleyn that show her in a suggestive manner, which could be seen as evidence of her romantic involvement with the king.
On the other hand, there is also evidence to suggest that Henry VIII did not have a sexual relationship with Mary Boleyn. For example, there are no records of Mary ever becoming pregnant, which would be expected if she had been having sex with the king. In addition, Mary's husband, William Carey, seems to have been unaware of any affair between his wife and the king.
Ultimately, the question of whether or not Henry VIII slept with Mary Boleyn is a matter of historical debate. There is evidence to support both sides of the argument, and it is unlikely that we will ever know for sure what the true nature of their relationship was.