We report the discovery of K2-98b (EPIC 211391664b), a transiting Neptune-size planet monitored by the K2 mission during its Campaign 5. We combine the K2 time-series data with ground-based photometric and spectroscopic follow-up observations to confirm the planetary nature of the object and derive its mass, radius, and orbital parameters. K2-98b is a warm Neptune-like planet in a 10 day orbit around a V = 12.2 mag F-type star with M ⋆ = 1.074 ± 0.042 M ⊙, R ⋆ = {1.311}-0.048+0.083 R ⊙, and age of {5.2}-1.0+1.2 {Gyr}. We derive a planetary mass and radius of M p = 32.2 ± 8.1 M ⊕ and R p = {4.3}-0.2+0.3 R ⊕. K2-98b joins the relatively small group of Neptune-size planets whose mass and radius have been derived with a precision better than 25%. We estimate that the planet will be engulfed by its host star in ∼3 Gyr, due to the evolution of the latter toward the red giant branch.