Yeah. 5. Nc3 is wrong. I was thinking the position after playing d3.
Now, random idea: Now that the d-pawns are gone, why not blocking the check with the Bc8 instead of the Bf8?
Either variation is still extremely favorable for white. The 7. Be3 line (not available with the immediate 4... Qxe4) seems somewhat better than the line with 7. Be2. If black doesn't play 7... Bb4+ immediately, white may play 8. Nc3 or 8. Nbd2, kicking the queen anyways (if 8... Bb4??, pinning the knight, white wins the bishop by playing a3 and b4 if the knight is in c3, and c3 if the kinght is in b2).
Pacman, the line has been already discussed in earlier posts: 4...d5 is better than Qxe4+ and W get only a slight advantage. Bc4 instead gives B serious problems in coordinating his forces. It's a quieter move but also more effective. Nxe5 looks dynamic but eliminates both the e-pawns, allowing B to play d5 with a decemt development.