  The transition metal chalcogenide Ta$_2$NiSe$_5$ undergoes a second-order
phase transition at $T_c=328$ K involving a small lattice distortion. Below
$T_c$, a band gap at the center of its Brillouin zone increases up to about
0.35 eV. In this work, we study the electronic structure of Ta$_2$NiSe$_5$ in
its low-temperature semiconducting phase, using resonant inelastic x-ray
scattering (RIXS) at the Ni $L_3$-edge. In addition to a weak fluorescence
response, we observe a collection of intense Raman-like peaks that we attribute
to electron-hole excitations. Using density functional theory calculations of
its electronic band structure, we identify the main Raman-like peaks as
interband transitions between valence and conduction bands. By performing
angle-dependent RIXS measurements, we uncover the dispersion of these
electron-hole excitations that allows us to extract the low-energy boundary of
the electron-hole continuum. From the dispersion of the valence band measured
by angle-resolved photoemission spectroscopy, we derive the effective mass of
the lowest unoccupied conduction band.
