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To accurately capture the impacts of nitrogen (N) on the land carbon (C) sink in Earth system models, model responses to both N limitation and ecosystem N additions (e.g., from atmospheric N deposition and fertilizer) need to be evaluated. The response of the land C sink to N additions depends on the fate of these additions: that is, how much of the added N is lost from the ecosystem through N loss pathways or recovered and used to increase C storage in plants and soils. Here, we evaluate the C-N dynamics of the latest version of a global land model, the Community Land Model version 5 (CLM5), and how they vary when ecosystems have large N inputs and losses (i.e., an open N cycle) or small N inputs and losses (i.e., a closed N cycle). This comparison allows us to identify potential improvements to CLM5 that would apply to simulated N cycles along the open-to-closed spectrum. We also compare the short- (<3 years) and longer-term (5-17 years) N fates in CLM5 against observations from 13 long-term N-15 tracer addition experiments at eight temperate forest sites. Simulations using both open and closed N cycles overestimated plant N recovery following N additions. In particular, the model configuration with a closed N cycle simulated that plants acquired more than twice the amount of added N recovered in N-15 tracer studies on short timescales (CLM5: 46 +/- 12 %; observations: 18 +/- 12 %; mean across sites +/- 1 standard deviation) and almost twice as much on longer timescales (CLM5: 23 +/- 6 %; observations: 13 +/- 5 %). Soil N recoveries in simulations with closed N cycles were closer to observations in the short term (CLM5: 40 +/- 10 %; observations: 54 +/- 22 %) but smaller than observations in the long term (CLM5: 59 +/- 15 %; observations: 69 +/- 18 %). Simulations with open N cycles estimated similar patterns in plant and soil N recovery, except that soil N recovery was also smaller than observations in the short term. In both open and closed sets of simulations, soil N recoveries in CLM5 occurred from the cycling of N through plants rather than through direct immobilization in the soil, as is often indicated by tracer studies. Although CLM5 greatly overestimated plant N recovery, the simulated increase in C stocks to recovered N was not much larger than estimated by observations, largely because the model's assumed C: N ratio for wood was nearly half that suggested by measurements at the field sites. Overall, results suggest that simulating accurate ecosystem responses to changes in N additions requires increasing soil competition for N relative to plants and examining model assumptions of C : N stoichiometry, which should also improve model estimates of other terrestrial C-N processes and interactions.