From this 2015 New York Post article:
Some 5 percent of Danish men have had sex with an animal.
That seems completely outlandish to me. Bestiality seems like a very rare fetish. It's probably wrong but you never know.
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TLDR: We don't know.
There really aren't any hard numbers on how many or few Danes have had sex with an animal.
The claim portrayed in the linked article most likely stems from a Danish television show called Danmark ifølge Bubber (Trans: "Denmark according to Bubber" Bubber is a Danish celebrity of sorts). In an interview, a veterinarian states in Danish.
I programmet interviewer Bubber en dyrlæge, som anslår, at 5-7 procent af danske mænd har haft sex med dyr, mens det gælder 0,5 procent af kvinderne.
probably 5 to 7 percent of Danish men have had sex with an animal, and probably 0.5% of women
In 2011, in the MetroXpress (a Danish newspaper, pp 10-11), Christian H. Hansen explains that no one really knows for sure:.
Han mener, at sex med dyr altid er en krænkelse af dyret, uanset om dyret tager skade af det eller ej. I øvrigt mener han, at det er naivt at tro, at dyrene ikke tager skade af det. Ingen ved, hvor udbredt dyresex er i Danmark
He believes, that sex with an animal always will be a violation, no matter if the animal suffers physical harm or not. Furthermore he believes that is is naive to think that animals aren't harmed from it. No one knows how widespread bestiality is in Denmark
Denmark's Animal Council released a report in 2006 in the lead up the eventual criminalization of bestiality in Denmark that further iterates the prevalence was unknown by experts:
De få undersøgelser, der er lavet, er behæftet med stor usikkerhed. Undersøgelserne er typisk foretaget på en udvalgt gruppe af mennesker, og givet emnets følsomme og tabubelagte natur er det usikkert, om svarene er helt sandfærdige. Resultaterne kan derfor højst give et indblik i forholdene hos de undersøgte grupper. Undersøgelserne belyser derfor ikke nødvendigvis, hvordan forholdene er i andre befolkningsgrupper eller for alle mennesker, der har seksuel omgang med dyr. Samtidig er undersøgelserne som nævnt primært baseret på personer fra den vestlige verden.
The few surveys, that have been done, are riddled with a large uncertainty. The surveys are usually done on a select group of people, and given the subjects sensitivity and taboo-like nature it is uncertain, whether the responses are completely truthful. The results can therefore at best give an insight into the preferences in the selected groups. The surveys do therefore not necessarily reflect, the actual circumstances in other groups of population, or for all people who are having sexual relations with animals. Furthermore the surveys are, as mentioned, mainly based on people of the western world in general.
There were claims in Danmark ifølge Bubber that some brothels in Denmark used to cater for bestiality, prior to the law change. I have not been able to find a reference supporting this. I have however found a very recent article in Altinget.dk (a reputable Danish newspaper) with the headline:
EU-enhed: Russiske medier spreder fake news om dyresex i Danmark / EU-unit: Russian media spreading fake news about animal-sex in Denmark
MISINFORMATION: Fake news om danske bordeller for dyresex spreder sig i Rusland. Formålet er at vise et Europa i moralsk forfald, siger EU's antipropaganda-agentur.
Misinformation. Fake news about Danish brothels for animal-sex is spreading in Russia. The purpose is to show a morally bankrupts Europe, says the EU's anti-propaganda-agency.
As to the credibility of the article from the New York Post, it is easy to question whether or not this is based on any kind of facts, or is more of an opinion piece, as there are multiple either flawed or false claims in the article, not related to the part about bestiality.
A very short list would include the claim that Danish people only work 28 hours a week (the normal work week is considered to be 37 hours)
Or that pharmacies are state-run. They are not, though you need a license from the state and appropriate education. You can get an aspirin at the supermarket or similar. The experience is not "like a trip to the DMV".