White has no advantage here, so its safe to assume that 5.Nxe5 is nothing special.
5.0-0 is the right move, when Black is alive, but not well.
I would also like to stress that whoever believes that the Exchange variation is "harmless" is simply uneducated. Black has just two ways to proven equality (4...dc6 5.0-0 Bg4 6.h3 h5 and 4...dc6 5.0-0 Qf6) but neither of them is clear of pits.
Recently Caruana fell into deep trouble against Najditch at the Grenke super-tournament employing the "solid" 5...Qf6 variation, which he handled rather poorly. Actually he won the game, but his position was certainly not enviable.
I thought Qd6 was a move.
Tim Taylor was advocating 4...bc6 in his Spanish repertoire book (on the modern Steinitz). I wasn't convinced at all, but then I wasn't convinced by any Taylor book...
The more I read this book the more I realize how much of it contains just plain wrong information. I need to go back to Amazon and update my review -- he will not be pleased.
In his KID book, he says 99.999% lines are winning for White in the FPA.