The Minuteman is a land-based intercontinental ballistic missile (ICBM). First flown in 1961, over 400 will remain in service until at least 2030. It is the first solid-fuel missile to have a digital flight control computer, a combination which enables a short-notice launch.
On 24 October 1974, a C-5A Galaxy successfully conducted an Air Mobile Feasibility Test when an 86,000-pound ICBM was extracted by parachute from the aircraft flying at 20,000 feet over the Pacific Ocean. As soon as the missile stabilized, its rocket engine fired. The 10-second engine burn allowed it to climb 12,000 feet before it dropped into the ocean as planned. Although only done once, it was enough to use as a negotiating point in the Strategic Arms Limitation Talks (SALT).
The C-5A in front of you, 69-0014, on display with this missile-launching trainer, is the aircraft that was flown to conduct those tests.