Spanish game question

Hi, I have a question about an interesting position in the Ruy Lopez, Schliemann defense. What would be the best response for Black after White takes the f-pawn? Would 5...d6 be a good response or is 5...Ne7 even better? Thanks in advance for your help!

This is what IM Andrew Greet says about 5.exf5 in his fantastic book 'Play the Ruy Lopez':

"The immediate 5 exf5 (he recommends 5.0-0 instead) is also possible, and may end up transposing after one of black's likely replies of 5...Be7, 5...d6 or 5...Bc5. The move 5...Ne7!? is interesting though."

According to my database, after 5 exf5, 5...d6 is the most popular move, followed by 5...Bc5, then 5...Ne7.

Although I play the Ruy Lopez, I seldom see the Schliemann, and even if I did, I play 5.0-0, so I guess I don't have enough credibility to answer your question if 5...Ne7 or 5...d6 is better. However, if you want to give a few more moves after 5...Ne7 or 5...d6, I would be happy to check it through with database!

5...Ne7-seems-best,but-i'm-no-Schliemann-expert.6O-O.c6.7Bc4.d6.8Re1.Bf5.9Bg5.Qd7.10Nc3.h6.11Bf6.gf6.anyone-got-a-recent-Schliemann-book?

 Thanks for the comments! I think 5...d6 is Blacks safest response because the e5-pawn needs to be protected. Otherwise 5...Bc5 looks very active. Does your database says something about that move too?

It doesn't really say anything, except that ...Ne7 and ...Bc5 is slightly better for white, while ...d6 is unclear

4.d3 is for people that wake up & don't feel like playing chess & feel like going for a draw, quote Nigel Short, I got a book called Gambiteer II, very good book about the Schliemann Gambit & the Albins Counter Gambit, when I get a bit of time, I'll post some of the answers to your questions, if I can a find them, yo! 

If you're gonna play Schliemann, you've gotta live with 4. d3. I've played it since I read Greet's book, and 4. ... Nf6 5. 0-0 also following his advice.

I suspect Nigel Short's feelings show a Schliemann player's disappointment at having the game steered in this deliberative direction. Which is why Greet recommended it.

Greet's book is amazingly good; I would not disagree with him lightly. But 5. exf5 actually seems pretty good to me. I'm surprised he didn't mention 5. ... a6 as a response, which you might want to consider. If white chooses to exchange the bishop and knight, black looks ok (maybe not quite good enough to compensate for the pawn); if white declines, black seems at least equal.

Of course we'll never know for sure...