Globular clusters are old stellar systems which exhibit very-high stellar densities in their cores. The globular cluster Terzan 5 is characterized by a high stellar encounter rate and hosts the largest detected population of millisecond pulsars. It also features bright GeV gamma-ray emission and extended X-ray radiation. However, no globular clusters have been detected in very-high-energy gamma rays (VHE, E> 100 GeV) so far. In order to investigate this possibility Terzan 5 has been observed with the H.E.S.S. telescope array in this energy band. The discovery of a source of VHE gamma rays from the direction of this globular cluster will be reported. The results of the VHE analysis and a multi-wavelength view of Terzan 5 will be presented in this contribution. No counterpart or model can fully explain the observed morphology of the detected VHE gamma-ray source.