When the meteor struck, humanity was forced to go to its backup plan.
They chose about 1000 of the fittest, smartest, and overall best men and women on the planet and brought them underground to the facility.
They locked them all in high-tech, cryogenic caskets, put them on ice, and programmed the base to automatically wake everyone up in 5000 years.
They were right to trust their technology. 5000 years later, after the rest of humanity had been extinguished, the facility's computers brought everyone back to consciousness right on schedule.
They were wrong, however, to trust themselves, for in their rush to put everyone under, they had forgotten to tell the computers to also unlock the caskets.