The nuclear binding energy arises from various effects that govern a nucleus’ properties. Different nucleon configurations within nuclear isomers lead to modified binding energies, often resulting in mass differences of tens to hundreds of kilo-electronvolts. These isomeric excitation energies can be directly accessed by measuring the difference in atomic masses of ground and isomeric states. Here, we present such measurements performed with the ISOLTRAP mass spectrometer at the radioactive ion beam facility ISOLDE/CERN using Penning trap and time-of-flight mass spectrometry. By evaluating the excitation energies of neutron-deficient indium isotopes at the N=50 shell closure against state-of-the-art shell model, DFT, and ab initio calculations, we contrast the performance of these theories applied to several nuclear properties. We further present searches for shape-coexistences close to N=50 through the precise excitation energy measurement of the (1/2)+ state in zinc-79, supported by accurate large-scale shell model calculations.