  We perform a systematic study of elliptic flow ($v_2$) in Au+Au collision at
$\sqrt{s_{NN}}=5$ GeV by using a microscopic transport model JAM. The
centrality, pseudorapidity, transverse momentum and beam energy dependence of
$v_2$ for charged as well as identified hadrons are studied. We investigate the
effects of both the hadronic mean-field and the softening of equation of state
(EoS) on elliptic flow. The softening of EoS is realized by imposing attractive
orbits in two body scattering, which can reduce the pressure of the system. We
found that the softening of EoS leads to the enhancement of $v_2$, while the
hadronic mean-field suppresses $v_2$ relative to the cascade mode. It indicates
that elliptic flow at high baryon density regions is highly sensitive to the
EoS and the enhancement of $v_2$ may probe the signature of a first-order phase
transition in heavy-ion collisions at beam energies of a strong baryon stopping
region.
