  We report on a seven-dimensional generator coordinate calculation in the two
deformation parameters $\beta$ and $\gamma$ together with projection on
three-dimensional angular momentum and two particle numbers for the low-lying
states in $^{76}$Kr. These calculations are based on covariant density
functional theory. Excellent agreement is found with the data for the spectrum
and the electric multipole transition strengths. This answers the important
question of dynamic correlations and triaxiality in a fully microscopic way. We
find that triaxial configurations dominate both the ground state and the quasi
$\gamma$-band. This yields a different picture from the simple interpretation
in terms of "coexistence of a prolate ground state with an oblate low-lying
excited state", which is based on the measured sign of spectroscopic quadrupole
moments. This study also provides for the first time a benchmark for the
collective Hamiltonian in five dimensions. Moreover, we point out that the
staggering phase of the $\gamma$-band is not a safe signature for rigid
triaxiality of the low-energy structure.
