  Isomers close to doubly-magic $^{78}_{28}$Ni$_{50}$ provide essential
information on the shell evolution and shape coexistence near the ${Z=28}$ and
${N=50}$ double shell closure. We report the excitation energy measurement of
the $1/2^{+}$ isomer in $^{79}_{30}$Zn$_{49}$ through independent
high-precision mass measurements with the JYFLTRAP double Penning trap and with
the ISOLTRAP Multi-Reflection Time-of-Flight Mass Spectrometer. We
unambiguously place the $1/2^{+}$ isomer at 942(10) keV, slightly below the
$5/2^+$ state at 983(3) keV. With the use of state-of-the-art shell-model
diagonalizations, complemented with Discrete Non Orthogonal shell-model
calculations which are used here the first time to interpret shape coexistence,
we find low-lying deformed intruder states, similar to other ${N=49}$ isotones.
The $1/2^{+}$ isomer is interpreted as the band-head of a low-lying deformed
structure akin to a predicted low-lying deformed band in $^{80}$Zn, and points
to shape coexistence in $^{79,80}$Zn similar to the one observed in $^{78}$Ni.
The results make a strong case for confirming the claim of shape coexistence in
this key region of the nuclear chart.
