analysis confusion question

Ok I might have figured this out.   I didn't understand why I would play Nxe5 and then let him play Fxe5 and basically just give him my Knight.   Chess.com had him not taking my knight and continuing as  4. Nxe5 Ne7 5. Nc4 Ng66. Qh5 Nc6 7. Ne3 Be7 8. Ncd5 O-O  

I am pretty sure my opponent would have taken my knight with his F pawn.  

After playing it through it looks like I would have actually taken his pawn and rook a few moves later.   

4... fxe5 5. Qh5+ g66. Qxe5+ Ne7 7. Qxh8

Looks like I need to look at all moves and see further ahead,    I didn't see that I could put him in check and force a move that would allow me to check and attack his Rook.

Let me know if my analysis is correct.

THANKS!! 

Please note: My comments are simply suggestions. I cannot be held liable for any loss of data, life or marbles due to following my instructions.

Whenever black plays an early …..Pe5 and …..Pf6, you should be looking to play Nxe5 as your first idea.

Doesn't always work. But if there is a quick win, usually begins with that.

@IMbacon,  the break down helps so much!!!

@varelse1 can you expand on your comment.   

My thought is maybe the sacrifice is worth because I will get the rook later or prevent him from castling and continue to make forcing moves waiting for a mistake   

For example if instead of 4. Bc4  I played below 

4. Nxe5 fxe5  5.Qh5+ g6 6.Qxe5+ while also attacking the Rook.       If he moves his King 5. e7 I can still play Qxe5+ without attacking the rook but many chances to keep forcing him.

Glad to help.