Recent wide-area surveys have enabled us to study the Milky Way with unprecedented detail. Its inner regions, hidden behind dust and gas, have been partially unveiled with the arrival of near-infrared (IR) photometric and spectroscopic data sets. Among recent discoveries, there is a population of low-mass globular clusters, known to be missing, especially towards the Galactic bulge. In this work, five new low-luminosity globular clusters located towards the bulge area are presented. They were discovered by searching for groups in the multidimensional space of coordinates, colours, and proper motions from the Gaia EDR3 catalogue and later confirmed with deeper VVV survey near-IR photometry. The clusters show well-defined red giant branches and, in some cases, horizontal branches with their members forming a dynamically coherent structure in proper motion space. Four of them were confirmed by spectroscopic follow-up with the MUSE instrument on the ESO VLT. Photometric parameters were derived, and when available, metallicities, radial velocities, and orbits were determined. The new clusters Gran 1 and 5 are bulge globular clusters, while Gran 2, 3 and 4 present halo-like properties. Preliminary orbits indicate that Gran 1 might be related to the Main Progenitor, or the so-called 'low-energy' group, while Gran 2, 3 and 5 appears to follow the Gaia-Enceladus/Sausage structure. This study demonstrates that the Gaia proper motions, combined with the spectroscopic follow-up and colour-magnitude diagrams, are required to confirm the nature of cluster candidates towards the inner Galaxy. High stellar crowding and differential extinction may hide other low-luminosity clusters.