Sleep means to rest your mind and body, usually at night. So it should be stative. But we often say something like "I am sleeping". So it looks also like a dynamic verb. Is sleep stative or dynamic or both?
Don't think of the names of the categories quite so literally. The University of Victoria's Study Zone specifically lists "sleep" as a dynamic verb, and from the description it should be pretty clear why:
Dynamic verbs (sometimes referred to as "action verbs") usually describe actions we can take, or things that happen
[S]tative verbs usually refer to a state or condition which is not changing or likely to change.
The difference is important, because stative verbs cannot normally be used in the continuous (BE + ING) forms.