October 5 is:
Rocky Mountain Oyster Day* (a delicacy in Colorado)
Rocky Mountain oysters, or mountain oysters, or meat balls, also known as prairie oysters in Canada, is a dish made of bull testicles. The organs are often deep-fried after being skinned, coated in flour, pepper and salt, and sometimes pounded flat.
National Apple Betty Day (a crustless apple pie seasoned with cinnamon, nutmeg, and sugar.)
Foodimentary.com says:
The apple is the fruit of the apple tree, species Malus domestica in the rose family (Rosaceae).
It is one of the most widely cultivated tree fruits, and the most widely known of the many members of genus Malus that are used by humans.
Apples grow on small, deciduous trees.
The tree originated in Western Asia, where its wild ancestor, Malus sieversii, is still found today.
Apples have been grown for thousands of years in Asia and Europe, and were brought to North America by European colonists.
1582 – Because of the implementation of the Gregorian calendar, October 5th did not exist in 1582 in Italy, Poland, Portugal and Spain.
Birthday of Jonathan Edwards (October 5, 1703), American theologian, philosopher, and college president who has been called “the greatest American mind of the Colonial Period”. He played a critical role in shaping the First Great Awakening.
1713 Birthday of Denis Diderot , French philosopher. He was a prominent figure during the Age of Enlightenment.
French Revolution: Women of Paris marched to Versailles in 1789 to confront Louis XVI about his refusal to abolish feudalism, to demand bread, and to have the King and his court moved to Paris.
French Revolution: Christianity was disestablished in France in 1793.
War of 1812: Battle of Thames in Canada; Americans defeated British and kill Shawnee leader, Tecumseh in 1813.
Birthday of Chester Alan Arthur (October 5, 1829), twenty-first President of the United States. He became president upon the death of Garfield. Suffering from poor health, Arthur made only a limited effort to secure the Republican Party’s nomination in 1884, and he retired at the end of his term. Journalist Alexander McClure wrote, “No man ever entered the Presidency so profoundly and widely distrusted as Chester Alan Arthur, and no one ever retired… more generally respected, alike by political friend and foe.”
1857 – The City of Anaheim, California was founded by fifty German families. Named for “Ana”, after the Santa Ana River, and “Heim”, the German word for “home”.
1905 – Wilbur Wright pilots Wright Flyer III in a flight of 24 miles in 39 minutes, a world record that stood until 1908.
1902 Ray Kroc was born in Oak Park, Illinois. Ray Kroc sold blenders for milkshakes, and one of his customers was a restaurant in San Bernardino, California owned by Maurice and Richard McDonald. Kroc set up a chain of drive-in restaurants based on their efficient assembly line production kitchen. He opened his first restaurant on April 15, 1955 in Des Plaines, Illinois. By 1961 he had 228 restaurants and he bought out the McDonald brothers. When he died in 1984 there were over 7,500 McDonald’s restaurants. Today there are over 36,000 restaurants in over 100 countries.
2001:
Barry Bonds of the San Francisco Giants broke Mark McGwire’s single-season home-run record when he hit his 71st and 72nd home runs of the season and finished the season with 73.
In 2022 – Aaron Judge of the NYY hit his 62nd home run of the season, besting the American League record set by Roger Maris in 1961.
2011: American businessman 
Steve Jobs, a pioneer of the personal computer era who co-founded Apple and transformed it into one of the world’s most successful companies, died at age 56.