Build estimate
Ryzen 5 5600 and RTX 4070 bottleneck estimate
The RTX 4070 is strong enough that the Ryzen 5 5600 can limit some 1080p high-refresh scenarios. The pair makes more sense at 1440p, where the GPU has enough rendering work to stay busy.
1080p
CPU bottlenecks are more likely here, especially in esports, strategy, simulation, and multiplayer games with heavy world updates. Raising graphics settings may not reduce the CPU limit, but it can use more GPU headroom.
1440p
This is the better target for the pair. The RTX 4070 is built for strong 1440p performance, and the Ryzen 5 5600 remains usable in many games if background tasks and thermals are under control.
Upgrade advice
If you already own this pair and play at 1440p, keep it unless a specific game shows poor frame pacing. For high-refresh 1080p, a faster CPU can be the more meaningful upgrade.