  We introduce an effective tight-binding model to discuss penta-graphene and
present an analytical solution. This model only involves the $\pi$-orbitals of
the sp$^2$-hybridized carbon atoms and reproduces the two highest valence
bands. By introducing energy-dependent hopping elements, originating from the
elimination of the sp$^3$-hybridized carbon atoms, also the two lowest
conduction bands can be well approximated - but only after the inclusion of a
Hubbard onsite interaction as well as of assisted hopping terms. The
eigenfunctions can be approximated analytically for the effective model without
energy-dependent hopping elements and the optical absorption is discussed. We
find large isotropic absorption of up to 24\% for transitions at the
$\Gamma$-point, but the general absorption will show a strongly anisotropic
behaviour depending on the linear polarization of the incident light.
