Is it possible to have five wisdom teeth?

Yes. Teeth in addition to the usual 32 are called supernumeraries, because that number is exceeded. These are often at the back of the jaws in line with the 3rd molars, or wisdom teeth. Some people do not get 3rd molars at all.
Supernumerary. The 4 would count as the wisdom teeth and any others are termed supernumerary. Not as uncommon as you would think. Good Luck.
Supernumerary teeth. Most people have four wisdom teeth, it is possible to have more and it is called supernumerary teeth.
Yes, it's possible. Genetics plays a role in the formation of extra teeth.
Wisdom teeth. Yes it is. In fact some people have any more than that. It's not very on though. I have seen a patient without any known syndrome with 8 wisdom teeth. It is sometimes hereditary and or ethnicity related. From my clinical experience, I have noticed more Black males with extra wisdom teeth but that's may just be anecdotal.
Yes. Although uncommon we can see patients with additional wisdom teeth. Most often they show up in the upper jaw above the normal wisdom teeth. Occassionally, we wil find extra ones on the lower arch.
Yes. Some people may present with more than four wisdom teeth. The extra tooth, or supernumerary tooth is often smaller in size than the wisdom tooth it is next to.
Yes. Yes. I've seen 8 in one patient. For best results, have your wisdom teeth managed by an oral surgeon.