Low-symmetry penta-PdPSe (Pd4P4Se4) with intrinsic in-plane anisotropy was synthesized successfully [P. Li et al., Adv. Mater., 2021, 2102541]. Motivated by this experimental discovery, we investigate the structural, mechanical, electronic, optical and thermoelectric properties of PdPSe nanosheets via density functional theory calculations. The phonon dispersion, molecular dynamics simulation, and cohesive energy mechanical properties of the penta-PdPSe are verified to confirm its stability. The phonon spectrum represents a striking gap between the high-frequency and the low-frequency optical branches and an out-of-plane flexure mode with a quadratic dispersion in the long-wavelength limit. The Poisson's ratio indicates that penta-PdPSe is a brittle nanosheet. The penta-PdPSe is a semiconductor with an indirect bandgap of 1.40 (2.07) eV using the PBE functional (HSE06 hybrid functional). Optical properties simulation suggests that PdPSe is capable of absorbing a substantial range of visible to ultraviolet light. Band alignment analysis also reveals the compatibility of PdPSe for water splitting photocatalysis application. By combining the electrical and thermal transport properties of PdPSe, we show that a high power factor is achievable at room temperature, thus making PdPSe a candidate material for thermoelectric applications. Our findings reveal the strong potential of penta-PdPSe nanosheets for a wide array of applications, including optoelectronic, water splitting and thermoelectric device applications.