Penta-graphene has recently been proposed as a new allotrope of carbon composed of pure pentagons, and displays many novel properties going beyond graphene [Zhang et al., Proc. Natl. Acad. Sci. U. S. A., 2015, 112, 2372]. To further explore the property modulations, we have carried out a theoretical investigation of the hydrogenated and fluorinated penta-graphene sheets. Our first-principles calculations reveal that hydrogenation and fluorination can effectively tune the electronic and mechanical properties of penta-graphene: turning the sheet from semiconducting to insulating; changing the Poisson's ratio from negative to positive, and reducing the Young's modulus. Moreover, the band gaps of the hydrogenated and fluorinated penta-graphene sheets are larger than those of fully hydrogenated and fluorinated graphene by 0.37 and 0.04 eV, respectively. The phonon dispersions and ab initio molecular dynamics simulations confirm that the surface modified penta-graphene sheets are dynamically and thermally stable, and show that the hydrogenated penta-graphene has more Raman-active modes with higher frequencies as compared to the fluorinated penta-graphene.