Opening Variation or Tactical Surprise?

I was not clear in my last post: Giuoco Piano Surprise. Sorry. 

I was playing against the computer as White and got the main line to the Giuoco Piano from Black until the computer played 5)...Bd6. I couldn't find this move in any of the Italian openings in my own database or books.

Is 1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4 (Bd6!?) a variation of some Italian opening or a tactical surprise by Black with Bd6?   How should White respond to 5)...Bd6? I lost too many pawns in the exchange! Thank you.

Below is a match from the chess.com database. It starts out as the Two Knights Defense, however, the position of pieces in my game and this match are identical after Black plays 5)...Bd6.

6de5.Ne5.7Ne5.Be5.8f4.Bd6.9e5.Qe7.10Qe2-looks-good.

 Thanks Coach! That's a very nice variation on the Giuoco Piano that I could not find in my thick books on openings. Well done.

Bump

Of course for this reason black should play 6...Bxe5. I would prefer not to capture on e5, which allows black to move his bishop which desperately needs to be moved. I would just continue with 6. O-O 7. Re1 8. Bg5 9. Nbd2, etc. Moves that develop. Black will have a very tough time developing and white should gain an advantage this way. 

thank you very munch for the post

I also cannot find 5...Bd6 in my opening books but there are a few games on Chess Assistant with this move and it does terrible for black , 22%. Noone over 2200 played 5...Bd6 in these games. White has 4 very good responses to it : 6 Bg5, 6 0-0 , 6 dxe5, 6 d5.

 in-the-6...Ne5.7Ne5.Be5.8f4.Ne4-line,9Qh5-looks-even-better.