The isobaric multiplet mass equation (IMME) relates the masses of an isospin multiplet quadratically, and it plays an important role in studies of nuclear structure, nuclear astrophysics, and fundamental symmetries. This work uses shell-model calculations, together with data from Ar decay and S(He,) experiments to provide an important step in explaining an observed IMME violation in the , quintet. It is shown that a small but finite cubic term is required for this case due to isospin mixing. The analysis also provides a means to obtain isospin nonconserving corrections for ArCl superallowed decay, which belongs to a category of decays that are used to extract the element of the CKM quark-mixing matrix.