  The isobaric multiplet mass equation (IMME) is known to break down in the
first T = 2, A = 32 isospin quintet. In this work we combine high-resolution
experimental data with state-of-the-art shell-model calculations to investigate
isospin mixing as a possible cause for this violation. The experimental data
are used to validate isospin-mixing matrix elements calculated with newly
developed shell-model Hamiltonians. Our analysis shows that isospin mixing with
nonanalog T = 1 states contributes to the IMME breakdown, making the
requirement of an anomalous cubic term inevitable for the multiplet.
