Achieving a low mean transverse energy or temperature of electrons emitted from the photocathode-based electron sources is critical to the development of next-generation and compact X-ray free electron lasers and ultrafast electron diffraction, spectroscopy, and microscopy experiments. In this Letter, we demonstrate a record low mean transverse energy of 5 meV from the cryo-cooled (100) surface of copper using near-threshold photoemission. Further, we also show that the electron energy spread obtained from such a surface is less than 11.5 meV, making it the smallest energy spread electron source known to date: More than an order of magnitude smaller than any existing photoemission, field emission, or thermionic emission based electron source. Our measurements also shed light on the physics of electron emission and show how the energy spread at few meV scale energies is limited by both the temperature and the vacuum density of states. © 2020 American Physical Society.