The tight-binding model is used in this study to examine the electronic and thermal properties of penta-Graphene (PG). To analyze these properties, approaches including the Kubo formula, linear response theory, and Green's function method are applied. The obtained numerical results show that by introducing bias voltage U, external magnetic field Π, and electron doping μ, significant modifications in electrical conductivity, magnetic susceptibility, and thermoelectric properties including power factor PF(T), Seebeck coefficients S(T), and figure of merit ZT(T) are observed. The band structure and density of states (DOS) of PG structure can be significantly altered by applying a bias voltage or an external magnetic field. The wide band gap of PG exhibited a marked reduction with the application of these external fields, displaying greater sensitivity to Π compared to U. Thermal properties of PG, including electrical conductivity σ(T), exhibit a peak as a function of temperature, which its peak position depends on the external fields and μ. Below the peak, σ(T) increases significantly with increasing external fields and μ, due to the reduced band gap and increased number of excited charge carriers, respectively. σ(T) demonstrates greater sensitivity to μ compared to Π, and both parameters have a more pronounced effect than bias voltage U. The magnetic field and bias voltage shift the peak position of the power factor PF(T) in opposite directions. Through tuning of the external fields, which alters the electronic structure of PG, the ZT(T) can be enhanced and its rate of increase is more dependent on bias voltage than on magnetic field.