  We study chaotic dynamics in a system of four differential equations
describing the dynamics of five identical globally coupled phase oscillators
with biharmonic coupling. We show that this system exhibits strange spiral
attractors (Shilnikov attractors) with two zero (indistinguishable from zero in
numerics) Lyapunov exponents in a wide region of the parameter space. We
explain this phenomenon by means of bifurcation analysis of the
three-dimensional Poincar\'e map for the system under consideration. We show
that the chaotic dynamics develop here near a codimension three bifurcation,
when a periodic orbit (fixed point in the Poincar\'e map) has the triplet $(1,
1, 1)$ of multipliers. As it is known, the asymptotic flow normal form for this
bifurcation coincides with the three-dimensional
Arneodo-Coullet-Spiegel-Tresser (ACST) system in which spiral attractors exist.
Based on this, we conclude that the additional near-zero Lyapunov exponent for
orbits in the observed attractors appear due to the fact that the corresponding
three-dimensional Poincar\'e map is close to the time-shift map of the
three-dimensional ACST-system.
