No, plants don't sleep, and neither do fungi or single celled organisms. Sleep seems to be a property specifically of animals.
https://pmc.ncbi.nlm.nih.gov/articles/PMC5120870/
4 and 5 don't seem to be exemplified by plants.
And you don't think different criteria might apply to plants? I mean, look, we are just discovering how plants function as a society. They are immobile and 4 and 5 might be caused by the fact that an animal is mobile, at least for the most examples, but where not, it can at least react in some manner. Plants have a very very slow reaction time so to them 4 and 5 don't apply even in waking condition, I mean unless you consider several hours to be a reaction. Let's be frank: we don't know (yet).
What I don't appreciate is an outright dismissal "plants do not sleep".