  Isobaric quintets provide the best test of the isobaric multiplet mass
equation (IMME) and can uniquely identify higher order corrections suggestive
of isospin symmetry breaking effects in the nuclear Hamiltonian. The
Generalized IMME (GIMME) is a novel microscopic interaction theory that
predicts an extension to the quadratic form of the IMME. Only the $A=20, 32$
$T=2$ quintets have the exotic $T_z = -2$ member ground state mass determined
to high-precision by Penning trap mass spectrometry. In this work, we establish
$A=36$ as the third high-precision $T=2$ isobaric quintet with the $T_z = -2$
member ground state mass measured by Penning trap mass spectrometry and provide
the first test of the predictive power of the GIMME. A radioactive beam of
neutron-deficient $^{36}$Ca was produced by projectile fragmentation at the
National Superconducting Cyclotron Laboratory. The beam was thermalized and the
mass of $^{36}$Ca$^+$ and $^{36}$Ca$^{2+}$ measured by the Time of Flight - Ion
Cyclotron Resonance method in the LEBIT 9.4 T Penning trap. We measure the mass
excess of $^{36}$Ca to be ME$ = -6483.6(56)$ keV, an improvement in precision
by a factor of 6 over the literature value. The new datum is considered
together with evaluated nuclear data on the $A=36$, $T=2$ quintet. We find
agreement with the quadratic form of the IMME given by isospin symmetry, but
only coarse qualitative agreement with predictions of the GIMME. A total of
three isobaric quintets have their most exotic members measured by Penning trap
mass spectrometry. The GIMME predictions in the $T = 2$ quintet appear to break
down for $A = 32$ and greater.
