I dug this book out of Dad's box back in the late 60's or early 70's.
The Valley of Creation by Edmond Hamilton. You may have read it in the 1964 Lancer edition (reissued in 1967) or the 1972 Lodestone edition. The quotations below are from the original publication in Startling Stories, July 1948, available at the Internet Archive; the text may differ somewhat from the book version.
A team of explorers or maybe mercenaries crashes in a remote valley (possibly China or Mongolia?)
They are mercenaries, and the setting is the China-Tibet border:
They five had been staff officers for Yu Chi Chan, the fat warlord who had held illegal sway over this remote southwestern province on the borders of Tibet.
They were, except for Li Kin, frank mercenaries who had taken many a warlord's pay. Nelson had been ten years in China, Nick Sloan nearly as long. Van Voss and the little Cockney were fugitive criminals, flotsam of China's civil wars.
There is no crash. The action takes place in a remote valley:
Eric Nelson sat up.
"You're no Tibetan," he said sharply, in that language.
"No," answered Shan Kar quickly. His accent was slurred as though he spoke an obscure dialect of Tibetan. He pointed through the open door at the gray, sunlit mountains in the distance.
"My people dwell there, in a valley called L'Lan. And we men and women of L'Lan have—enemies.
and discover people living there that are bonded with telepathic animals--
"Necessary—to torture a dumb animal?" Nelson snapped.
"He can tell me what I must know," Shan Kar retorted. "And he is no dumb animal. He is of the Brotherhood, of our enemies."
"Blimey, the man's cracked!" exclaimed Lefty Wister.
Shan Kar disregarded them all. He was staring fixedly into the splendid eyes of the wounded bird.
Nelson almost thought he could hear question and answer, inside his mind. Telepathic questions put by Shan Kar—and stubborn, defiant answer by the crippled eagle!
Could man and beast talk telepathically? His weird dream flashed back into his memory. Shar Kan, eyes narrowing, suddenly twisted the crippled wing again. A spasm of agony shook the eagle.
wolves, tigers, horses and eagles I think.
"However it was done," Shan Kar went on, "the fact remains that in this valley the four higher beast-races, the wolf and tiger and horse and eagle, are in some ways the mental equals of man. And those four clans claim their intelligence entitles them to absolute equality with the human race.
"In fact, they even claim that their races and the human race were created equal in intelligence, that in the dawn of time they issued equally from the Cavern of Creation!"
They eventually discover that the source of the telepathic bond is a cave, that turns out to be a crashed UFO buried in the mountainside,
"A ship," he whispered. "The Cavern is a giant ship, that crashed here heaven knows how long ago. A space ship, that came to Earth and fell and was buried here by the silt of ages."
emitting some type of radiation
Nsharra drew him back. "Do not go too close to the cold fire—its light can blast and kill!"
"Radioactive!" Nelson muttered incredulously. "A radioactive chemical mass of some sort that's eaten its way into the floor."
Very effectively, that moat of death had barred all entrance into the unguessable farther depths of the Cavern.
that has mutated humans and animals alike.
It wasn't the radiation. The aliens left a telepathic message for posterity, saying in part:
"So we built this star-ship, and in it the last remnants of our race went out from our dying planet into the stars to find another world. We searched star-system after star-system without finding a world that fitted us—until at last a disastrous accident in space crippled our star-ship as it neared this System.
"Our crippled ship crashed upon this planet, in this valley. It could never fly again. And we could not build another ship for we were dying. This world was wrong for us, its atmosphere and chemical composition poisoned us and that poison in our bodies left us not long to live.
"We knew that we were doomed. Yet we could not let all the hard-won intelligence and knowledge of our race thus perish! Therefore we determined that, though our bodies were dying, our minds should continue to live upon this planet.
"They could only do so, if we transferred our minds into the bodies of creatures native to this world. Only the higher creatures could house our minds. So we picked five different species from among them, the ape and the tiger and the horse and the wolf and eagle.
"At least one of those differing species, we hoped, would survive even if the others perished. So we took members of those clans and we so altered their brain-structure as to give them the power of telepathic speech and so altered their genes as to make the change hereditary. Then we transferred our minds into their bodies.
"Now that has been done. We wear the new bodies of the five Clans and our old bodies are dead. We go out now from this wrecked ship to begin again the struggle against nature on this planet.