Two-dimensional pentagonal structures based on the Cairo tiling are the basis of a family of layered materials with appealing physical properties. In this work we present a theoretical study of the symmetry-based electronic and optical properties of these pentagonal materials. We provide a complete classification of the space groups that support pentagonal structures for binary and ternary systems. By means of first-principles calculations, the electronic band structures and the local spin textures in momentum space are analyzed for four examples of these materials, namely, PdSeTe, PdSeS, InP5 and GeBi2, all of which are dynamically stable. Our results show that pentagonal structures can be realized in chiral and achiral lattices with Weyl nodes pinned at high-symmetry points and nodal lines along the Brillouin zone boundary; these degeneracies are protected by the combined action of crystalline and time-reversal symmetries. Additionally, we computed the linear and nonlinear optical features of the proposed pentagonal materials and discuss some particular features such as the shift current, which shows an enhancement due to the presence of nodal lines and points, and their possible applications.