Neutron-rich, radioactive Zn isotopes were investigated at the Radioactive Ion Beam facility REX-ISOLDE (CERN) using low-energy Coulomb excitation. The energy of the 21+ state in Zn78 could be firmly established and for the first time the 2+→01+ transition in Zn80 was observed at 1492(1) keV. B(E2,21+→01+) values were extracted for Zn74,76,78,80 and compared to large scale shell model calculations. With only two protons outside the Z=28 proton core, Zn80 is the lightest N=50 isotone for which spectroscopic information has been obtained to date. Two sets of advanced shell model calculations reproduce the observed B(E2) systematics. The results for N=50 isotones indicate a good N=50 shell closure and a strong Z=28 proton core polarization. The new results serve as benchmarks to establish theoretical models, predicting the nuclear properties of the doubly magic nucleus Ni78. © 2007 The American Physical Society.