The new era of space exploration demands a significant increase in the number of human and robotic missions, thus resulting in novel communication and service requirements. To satisfy such requirements, the fifth generation of mobile communication systems (5G), despite providing connectivity on Earth, has the potential to serve as a communication standard for space resource missions, particularly the ones targeting the Moon. In fact, 5G non-terrestrial networks (NTNs) are already in the standardization process and new techniques are being proposed in order to counteract the peculiarities of the nonterrestrial channel. However, going one step ahead and deploying constellations of satellites around the Earth or the Moon, requires first a detailed analysis and testing of the validity of the proposed techniques. Therefore, in this paper, we introduce the 5G Space Communications Lab, which has been developed with the purpose of simulating space-based 5G communications. The designed testbed proposed here increases the technology readiness level (TRL) of NTN-based 5G systems, demonstrating over a laboratory environment successful 5G communication via space links.