We studied the physical, electronic transport and optical properties of a unique pentagonal PdQ2 (Q= S, Se) monolayers. The dynamic stability of 2D - wrinkle like - PdQ2 is proven by positive phonon frequencies in the phonon dispersion curve. The optimized structural parameters of wrinkled pentagonal PdQ2 are in good agreement with the available experimental results. The ultimate tensile strength (UTHS) was calculated and found that, penta-PdS2 monolayer can withstand up to 16% (18%) strain along x (y) direction with 3.44 GPa (3.43 GPa). While, penta-PdSe2 monolayer can withstand up to 17% (19%) strain along x (y) dirrection with 3.46 GPa (3.40 GPa). It is found that, the penta-PdQ2 monolayers has the semiconducting behavior with indirect band gap of 0.94 and 1.26 eV for 2D-PdS2 and 2D-PdSe2, respectively. More interestingly, at room temperacture, the hole mobilty (electron mobility) obtained for 2D-PdS2 and PdSe2 are 67.43 (258.06) cm2 V-1 s-1 and 1518.81 (442.49) cm2 V-1 s-1, respectively. In addition, I-V characteristics of PdSe2 monolayer show strong negative differential conductance (NDC) region near the 3.57 V. The Shockly-Queisser (SQ) effeciency prameters of PdQ2 monolayers are also explored and the highest SQ efficeinciy obtained for PdS2 is 33.93% at -5% strain and for PdSe2 is 33.94% at -2% strain. The penta-PdQ2 exhibits high optical absorption intensity in the UV region, up to 4.04 × 105 (for PdS2) and 5.28 × 105 (for PdSe2), which is suitable for applications in optoelectronic devices. Thus, the ultrathin PdQ2 monolayers could be potential material for next-generation solar-cell applications and high performance nanodevices.