Story highlights PETA: This is the first lawsuit seeking constitutional protection against slavery for non-humans

The complaint alleges that five killer whales are SeaWorld slaves

SeaWorld calls the lawsuit a baseless publicity stunt

Can killer whales sue SeaWorld for enslavement?

A lawsuit filed Wednesday by People for the Ethical Treatment of Animals and other "next friends" of five SeaWorld killer whales takes that novel legal approach.

The 20-page complaint asks the U.S. District Court in Southern California to declare that the five whales -- Tilikum, Katina, Corky, Kasatka, and Ulises -- are being held in slavery or involuntary servitude in violation of the 13th Amendment.

A PETA statement said the lawsuit is the first of its kind in contending that constitutional protections against slavery are not limited to humans.

"Plaintiffs were forcibly taken from their families and natural habitats, are held captive at SeaWorld San Diego and SeaWorld Orlando, denied everything that is natural to them, subjected to artificial insemination or sperm collection to breed performers for defendants' shows, and forced to perform, all for defendants' profit," the lawsuit says, arguing that those conditions amount to enslavement and/or forced servitude.

JUST WATCHED PETA: SeaWorld enslaves killer whales Replay More Videos ... MUST WATCH PETA: SeaWorld enslaves killer whales 02:03

A SeaWorld statement called the lawsuit a baseless publicity stunt by PETA, which is known for provocative advertisements and public demonstrations on behalf of animal rights.

At the heart of the lawsuit is the question of whether a non-human entity can sue for a violation of constitutional rights.

The 13th Amendment outlaws slavery and "involuntary servitude" in the United States without any specific mention that it applies only to people.

"Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction," says the amendment's first section.

In its statement, PETA called the lawsuit "the first ever seeking to apply the Thirteenth Amendment to non-human animals."

The lawsuit seeks an order for the release of the whales "from bondage" and a permanent order against holding them in slavery, as well as appointment of a legal guardian to carry out the transfer of the whales to a suitable habitat.

In addition, it seeks attorneys' fees and costs.

The "next friends" joining PETA in representing the killer whales are three marine mammal experts, including Ric O'Barry, who was featured in the Academy Award-winning documentary "The Cove" about dolphin-hunting in Japan, and two former Sea World trainers.

Their lawsuit contends killer whales -- Orcinus orca, the largest species of the dolphin family -- "possess sophisticated learning, problem solving, and communicative abilities," as well as "distinctive cultural traits."

In a statement responding to the lawsuit, SeaWorld Parks and Entertainment said the court case challenges "the public's right to enjoy and learn more about marine mammals."

"This effort to extend the Thirteenth Amendment's solemn protections beyond human beings is baseless and in many ways offensive," the statement says.

SeaWorld is "among the world's most respected zoological institutions," it continues, adding that SeaWorld parks "are fully accredited by the Association of Zoos and Aquariums and the Alliance of Marine Mammal Parks and Aquariums" with legal permission to display marine mammals.

"PETA has once again showed that it prefers publicity stunts to the hard work of caring for, rescuing and helping animals," the SeaWorld statement said.

State and federal courts have traditionally understood laws dealing with animal ownership and cruelty as applying only to human actions, meaning the animals themselves could neither be prosecuted nor act as plaintiffs or defendants.

That would include litigation and legislation involving hunting and breeding of animals and plants, as well as zoo and circus displays.