  The only proposed observation of a discrete, hexacontatetrapole ($E6$)
transition in nature occurs from the T$_{1/2}$ = 2.54(2)-minute decay of
$^{53m}$Fe. However, there are conflicting claims concerning its $\gamma$-decay
branching ratio, and a rigorous interrogation of $\gamma$-ray sum contributions
is lacking. Experiments performed at the Australian Heavy Ion Accelerator
Facility were used to study the decay of $^{53m}$Fe. For the first time,
sum-coincidence contributions to the weak $E6$ and $M5$ decay branches have
been firmly quantified using complementary experimental and computational
methods. Agreement across the different approaches confirms the existence of
the real $E6$ transition; the $M5$ branching ratio and transition rate have
also been revised. Shell model calculations performed in the full $pf$ model
space suggest that the effective proton charge for high-multipole, $E4$ and
$E6$, transitions is quenched to approximately two-thirds of the collective
$E2$ value. Correlations between nucleons may offer an explanation of this
unexpected phenomenon, which is in stark contrast to the collective nature of
lower-multipole, electric transitions observed in atomic nuclei.
