Is the incident of the Prophet (peace be upon him) placing his thumb on the necks of five horses, which resulted in a mark called "the Khamsa" and indicates the horse's authenticity, mentioned in any of the books of Hadith? And what is its original source, if true?

There is no basis for the story that the Prophet, peace and blessings be upon him, placed his thumb on some horses to mark them as authentic. None of the scholars or those who wrote about horses mentioned it. What was mentioned about the Prophet's horses is that their number was five or seven, and their names were As-Sakb, Lazaz, Al-Murtajiz, Al-Luhayf, Ad-Dars, Mulawih, and Al-Ward.

Some desirable descriptions of horses were mentioned in the Prophetic Sunnah, among them: "The best of horses are the jet-black, with a white blaze, a white upper lip, three white socks, and the right foreleg free of white, and if not jet-black, then a dark bay with these markings." The shikal (uneven white markings on the legs) in horses is disliked, which is when three legs have white markings and one is free, or vice versa.

The stories of the lineages of Arabian horses and their origins mentioned by Ibn Al-Kalbi are tales for which there is no sound chain of transmission, and the lineages of these horses were well-known before Islam.