  Recent measurements and hydrodynamic model calculations suggest that the
higher-order flow coefficients $v_{4}$ and $v_{5}$ have two contributions: a
linear contribution driven by the initial-state eccentricities,
$\varepsilon_{n}$, and a mode-coupled contribution derived from the lower-order
eccentricity coefficients $\varepsilon_{2}$ and $\varepsilon_{3}$. Measurements
of these two contributions to $v_{4}$ and $v_{5}$ provide crucial insights to
discern initial-state models and to constrain the temperature-dependent
specific shear viscosity, $\eta/s$, of the plasma produced in heavy-ion
collisions. In this work, we have employed the two-subevents cumulant technique
to provide the first beam-energy and collision-system dependence of the linear
and mode-coupled contributions to the higher-order flow harmonics. Our results
are shown and discussed for several centrality intervals for U+U collisions at
$\mathrm{\sqrt{s_{NN}}}$= 193 GeV, Au+Au collisions at
$\mathrm{\sqrt{s_{NN}}}$=200, and 54.4 GeV and Cu+Au collisions at
$\mathrm{\sqrt{s_{NN}}}$=200 GeV. The results are compared with similar studies
performed by the ALICE experiment at LHC.
