Your game avoids the Fried Liver; it does not beat it. The line that you reject beginning with 5...Nxd5 is the Fried Liver. Most players avoid fried liver because the flavor is strong, despite its nutritional value. I prefer it with grilled onions, but also avoid it in most OTB games. I avoid it by playing 1...e6.
Here's a short game where I show a pretty good alternative to responding to the Fried Liver Attack.
In the forums, so far I only have seen the move 3...h6 (the "anti friend liver") as well as some other responses, which I will show.
If you think those responses are the only way to deal with the Fried Liver Attack, then here's an alternative suggestion.