I will be nice to you since I'm afraid it will hurt your feelings.
Higher FPS does mean less input lag. But there is a restriction, a cap, a limitation as to your eyes and the monitor can deliver.
Hertz does not equal Frame per Second or FPS. Regular monitors have 60hz while regular GAMING monitors have 144hz. Just recently Alienware introduced 240hz monitors where most pro players play in right now. I highly doubt that a lot of people are using 240hz right now. I use 144hz myself and I believe if you are at least global you would use one too. This hertz is the capability of monitors to deliver images/second.
One thing you would want to avoid is having FPS drop or where the low 1% percentile of your FPS drop below 60FPS threshold (standard monitor), 144FPS (gaming), or 240hz (alienware). In those instances, you will experience frame skipping. Hence, as long as your 1% is above 240fps with a 240hz monitor you're doing fine and you will not experience any disadvantage nor any advantage from having 5000fps.
The reason people want their FPS to be as high as they could is because they want their 1% to be above the monitor threshold. Which normally is 144hz.
So did you learn something today?