The electronic structure of monolayer pentagonal palladium diselenide (PdSe2) is analyzed from the topological band theory perspective. Employing first-principles calculations, effective models and symmetry indicators, we find that the low-lying conduction bands are topologically nontrivial, protected by time reversal and crystalline symmetries. Numerical evidence supporting the nontrivial character of the bands is presented. Furthermore, we obtain a relevant physical response from the topological viewpoint, such as the spin Hall conductivity.