I know this variation as the Anderssen variation. or the 
Anderssen-Smyslov variation. One of the better replies (and the one I favour personally) is 5.....Bc5. This reply appeared first in two games Anderssen-Morphy (2nd and 4th match game, 1858 ). 
In more modern times it has appeared in the games of the 1...e5 specialist Ivan Sokolov, Emms and in the games of Pomariov.

The position after 6.0-0 is mostly recorderd under ECO78 as it transposes from 5.0-0, Bc5 6.d3
In this position 6...0-0 doesnt give black much compensation for the pawn sack.
Black should reply either I.6....b5 7.Bb3,d6 (Emms) or II..6....d6 (Sokolov, Timman)

These variations differ slightly where the response to the move Be3 is concerned, ..d6 the more
flexibel response. Note that ommitting the move b5 may give the game a more italian character.

I. 5.d3,Bc5 6.0-0, b5 7.Bb3, d6 8.Be3, 0-0 as Bxc5 is hardly a positional threat.
II. 5.d3,Bc5 6.0-0, d6 7.Be3, Bxe3 seem OK as well (while a transposition to var. I with 7...b5 is still possible).


5.d3,d6 leads to positions that may be considered as belonging to the Deferred Steinitz defence.
As for 5.d3, d6 the following games are worth looking into:

5.d3, d6 6.c3,g6 7.0-0, Bg7
Smyslov-Euwe, Groningen 1946  (8.Re1,b5)
Boleslavsky-Smyslov!, USSR, 1947 (8.Re1,0-0 9.Nbd2,Na5)
Cholmov-Korchnoi, USSR-team, 1962 (8.Re1,0-0 9.Nbd2,Nd7)
Stein-Korchnoi, USSR, 1964 (8.d4?!,0-0 9.d5,Ne7)

5.d3, d6 6.c3,g6 7.Nbd2,Bg7 8.Nf1!?, 0-0
Smyslov-Boleslavsky, USSR, 1943 

5.d3,d6 6.c3, Be7!? 7.0-0,0-0 8.Nbd2,Nd7!
Smyslov-Geller, USSR, 1960 
Bronstein-Geller, USSR, 1963 

5.d3,d6 6.c3, Be7 7.Nbd2, 0-0 8.Nf1!?,b5 9.Bb3
Fischer-Smyslov, Havanna, 1965

I play the open lopez and i'm always happy to see 5.d3. I play d6,g6,Bg7,O-O and then b5! and Nb8 with Nbd7,Bb7 and eventually d5. It ssems stupid to post so many moves for black but none for white but in all ny games that's exactly the moves made by black because usyally white plays c3,Nd2,Nf1,Ng3 etc. I believe that the plan with d3 and c3 is much stronger after black plays Be7 and d6 of course!

After 5.d3 Bc5 6.0-0 (but not 6.Bxc6 dxc6 7.Nxe5?? Qd4 of course) 0-0 (d6 or b5) I have found 44 games, 24 seeing 7.Bxc6, 16 of them White winning. After 5.d3 Be7 6.Bxc6+ White's results even have been better: 20 wins out of 24. So I suppose you are right.