Can Black defend in this difficult position? Can Black reach solid and defensible position in the below diagram? I understand that Black will have to apply &quot;equalize over time&quot; method, so to help posters keep the analysis brief, I am interested in position that offers realistic chances to reach equality over time.
[Title &quot;Black to move&quot;]
[StartFlipped &quot;0&quot;]
[fen &quot;r3kb1r/ppp1pppp/n4n2/1N1P5/8/4B3/PPP1NPPP/2KR3R b kq - 0 1&quot;]
I'd like to point out that I tend to post Stockfish's entire tree of moves, but anything past the first 4 or 5 full moves is likely fiction.

To answer the OP's question, the answer is "with perfect play, Black looks lost. However, Black is not so lost he can't offer resistance."  Giving up on the game makes no sense to me since imperfect play got Black into this situation to begin with. With staunch resistance, perhaps White will err as Black did previously.

EDIT -
1... Nxd5 2. Rxd5 c6 3.Re5 and black is lost` variation shows White's advantage dropping to .5

The ever-practical Stockfish sees the following after several minutes. It decides that the d5 pawn is the problem and removes it. In the main line, White ends up with a 1 point advantage. The good news is that Black is well positioned to defend.

In the 1...Nxd5 variation, Stockfish says White is slightly better than the main-line.  I'm going to have to look at this one a bit more. It's... odd.

In the variation at move 3, Stockfish rates the final position as -.5, but I don't see how Black's extra piece is going to save him from the pawn onslaught.

[Title "Black to move (Stockfish)"]
[StartFlipped "0"]
[fen "r3kb1r/ppp1pppp/n4n2/1N1P5/8/4B3/PPP1NPPP/2KR3R b kq - 0 1"]

1... e6 (1...Nxd5 2.Rxd5 c6 3.Rd2 (3.Re5 cxb5 4.Rxb5 b6 5.Rd5 Nb4 6.Rd2 e6 7.Nc3 Rd8 8.Rhd1 Rxd2) cxb5 4.Rhd1 b4 5.Bxa7 e6 6.Bb6 h5 7.Rd7 h4) 2.dxe6 fxe6 3.Rhe1 ( 3.Nxa7 c6 4.Nd4 Bc5 5.Ndxc6 Bxe3+ 6.fxe3 bxc6 7.Nxc6 Rf8 8.Rhf1 Ng4 9.Rxf8+ Kxf8 10.b4 Nxe3 11.Rd3 Nd5 12.Rf3+ Ke8 13.a3 Kd7 14.Ne5+ Kd6 15.Nc4+ Ke7 16.Kb2 Nf6 17.Rg3 g6 18.Rd3 Nc7 19.Ne5 Ncd5 20.c4 Nf4 21.Nc6+ Kf7 )Kf7 4.Ng1 c6 5.Nd4 e5 6.Nb3 b6 7.Nf3 Re8 8.Kb1 Nb4 9.Nbd2 e4 10.Nd4 Rd8 11.a3 c5 12.Nb5 Nc6 13.h3 Be7 14.Nc3 h6 15.Ndxe4