  We show that minimal boson stars, i.e. boson stars made out of scalar fields
without self-interaction, are always classically unstable in 5 space-time
dimensions. This is true for the non-rotating as well as rotating case with two
equal angular momenta and in both Einstein and Gauss-Bonnet gravity,
respectively, and contrasts with the 4-dimensional case, where classically
stable minimal boson stars exist. We also discuss the appearance of ergoregions
for rotating boson stars with two equal angular momenta. While rotating black
holes typically possess an ergoregion, rotating compact objects without
horizons such as boson stars have ergoregions only in a limited range of the
parameter space. In this paper, we show for which values of the parameters
these ergoregions appear and compare this with the case of standard Einstein
gravity. We also point out that the interplay between Gauss-Bonnet gravity and
rotation puts constraints on the behaviour of the space-time close to the
rotation axis.
