An Ending to Analyze

In the diagram I played 56.Kxf5 and after 56...Rxd3 ended up losing. Black got his 2P’s advanced far enough that he was able to sac his R for my f-Pawn and queen one of his own which my lone R couldn’t stop. Was 56.Ne5 any better?

I don’t know. I tried analyzing this position with an engine without much success because too much is beyond the engine’s horizon to correctly evaluate the position and I’m just not good enough to know what the result should be. Maybe somebody who is actually interested in studying chess and trying to improve wants to tackle it. These days such analysis is more work than I want to do.