1. The Battle of Bennington: On October 5, 1777, New Hampshire troops under the command of General John Stark joined forces with soldiers from Vermont and Massachusetts to defeat a British detachment at the Battle of Bennington in present-day Vermont. The victory boosted morale for the American army during the Revolutionary War.

2. The First NH State Fair: The first New Hampshire State Fair was held on October 5, 1875, in Manchester. The event attracted a large crowd of farmers, craftsmen, and exhibitors who displayed their products and skills, including prize-winning livestock, homegrown vegetables, and handcrafted items.

3. First Telephone Exchange: On October 5, 1877, the first telephone exchange in New Hampshire opened in Nashua. The service allowed users to make local and long-distance calls, connecting people across the state and beyond.

4. The Scopes Trial: On October 5, 1925, the Scopes Trial began in Dayton, Tennessee, but it had implications for New Hampshire as well. The trial put the spotlight on the debate over the teaching of evolution in public schools. In 1927, New Hampshire passed a law that prohibited the teaching of evolution in schools.

5. The Mount Washington Cog Railway: On October 5, 1869, the Mount Washington Cog Railway officially opened in New Hampshire. The railway, which is still in operation today, is the world's first mountain-climbing cog railway and offers breathtaking views of the White Mountains.