The renormalization-group functions governing the critical behavior of the three-dimensional weakly-disordered Ising model are calculated in the five-loop approximation. The random fixed point location and critical exponents for impure Ising systems are estimated by means of the Padé-Borel-Leroy resummation of the renormalization-group expansions derived. The asymptotic critical exponents are found to be γ = 1.325 ± 0.003, η = 0.025 ± 0.01, ν = 0.671 ± 0.005, α = -0.0125 ± 0.008, β = 0.344 ± 0.006, while for the correction-to-scaling exponent, a less accurate estimate ω = 0.32 ± 0.06 is obtained.