  Masses of $^{52}$Co, $^{52}$Co$^m$, $^{52}$Fe, $^{52}$Fe$^m$, and $^{52}$Mn
have been measured with the JYFLTRAP double Penning trap mass spectrometer. Of
these, $^{52}$Co and $^{52}$Co$^m$ have been experimentally determined for the
first time and found to be more bound than predicted by extrapolations. The
isobaric multiplet mass equation for the $T=2$ quintet at $A=52$ has been
studied employing the new mass values. No significant breakdown (beyond the
$3\sigma$ level) of the quadratic form of the IMME was observed
($\chi^2/n=2.4$). The cubic coefficient was 6.0(32) keV ($\chi^2/n=1.1$). The
excitation energies for the isomer and the $T=2$ isobaric analogue state in
$^{52}$Co have been determined to be 374(13) keV and 2922(13) keV,
respectively. The $Q$ value for the proton decay from the $19/2^-$ isomer in
$^{53}$Co has been determined with an unprecedented precision, $Q_{p} =
1558.8(17)$ keV. The proton separation energies of $^{52}$Co and $^{53}$Ni
relevant for the astrophysical rapid proton capture process have been
experimentally determined for the first time. \end{abstract}
