  We study the quasinormal modes (QNMs) of a charged scalar field on a
Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS$_{5}$) black hole in the small
radius limit by using the isomonodromic method. We also derive the
low-temperature expansion of the fundamental QNM frequency. Finally, we provide
numerical evidence that instabilities appear in the small radius limit for
large values of the charge of the scalar field.
