Was the movie "The Prince and Me 2" well researched to say that the Danish monarchy was five thousand years old?

Unlikely - it was not unified until the 10th Century AD - and the earliest monarchy probably goes back only a couple of centuries before that. That's how it goes with movies.

Hopefully, at least you don't have people with zippers in their clothing as in the 15th century travesty of a tv series, The White Queen.

Actually the Danish monarchy is older than the British monarchy in the Vikings/ Norsemen brought over their system of kingship to the British isles.

Britain was a fragmented loose random group of tribes led by warlords constantly at war with each other. The Vikings came over conquered everybody and then brought everyone together to elect one overall king. That brought peace. The Vikings became Christians and that became the religion of the country.

the system has been in place in this country for over a thousand years.

Denmark was one of the most powerful nations on earth in 1000 A.D., but I doubt their monarchy claims can go more than 1000 years earlier than that.