4..Nxe4 is just met with 5.Nxe4!!
4..Nxe4 is a blunder. It blunders the knight. You don't need to take on f7 at all on move 5.
In your variation black mates white on f2 only because white blundered because they took on f7. Terrible. The truth hurts.
4...Nxe4?? is a blunder, and the same goes for 5.Nxe4?? d5, and Black gets back the piece with a large advantage.
Correct is 5.Bxf7+ Ke7 6.d4! (6.d3 also goes) when the g5 knight is taboo.
To the O.P.:
5...b5 Ulvestad variation. Both the Fritz and the Ulvestad lead by best play to the same position, which is better for White (a pawn up with Black having not quite adequate compensation).
No, because (6 Bf1) 6...Nd4 is not obligatory in the Ulvestad. Black can play 6...Nxd5 7 Bxb5 Bb7 and has quite acceptable compensation; e.g. 8 d4 exd4 9 0-0 Be7 10 Qh5 g6 11 Qh6 Qd7 12 Re1 a6! 13 Ba4 Qf5 14 Nf3 0-0-0 15 Bxc6 Bxc6 16 Nxd4 Qf6 and so on.
5...b5 Ulvestad variation. Both the Fritz and the Ulvestad lead by best play to the same position, which is better for White (a pawn up with Black having not quite adequate compensation).
No, because (6 Bf1) 6...Nd4 is not obligatory in the Ulvestad. Black can play 6...Nxd5 7 Bxb5 Bb7 and has quite acceptable compensation; e.g. 8 d4 exd4 9 0-0 Be7 10 Qh5 g6 11 Qh6 Qd7 12 Re1 a6! 13 Ba4 Qf5 14 Nf3 0-0-0 15 Bxc6 Bxc6 16 Nxd4 Qf6 and so on.
Looks like an interesting (and rare) option. Thanks!
It is simple! DO NOT ALLOW THE FRIED LIVER! I still to this day why so many idiots take the pawn!
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5?! d5 5.exd5 Na5! (NOT 5...Nxd5????, allowing the Fried Liver).
White has nothing!
white has equality, an equality lower rated players fail to appreciate.
1.learn the theory on the 4...d5 line
2. dont play nf6 this early and play bc5, be7 or even d6.
3. dont play e5 vs e4.
Looks like an interesting (and rare) option. Thanks!
See my book for more details 
https://everymanchess.com/products/a-disreputable-opening-repertoire
...in which you get a mention btw...
"I was intending initially to write about the Traxler, my main weapon for over thirty years. Unfortunately, issues have arisen with 4...Bc5, not least 5 d4! for which IM Panayotis Frendzas has been proselytizing online. It seems the best Black can do is to try to defend a dreary endgame a pawn down after 5...d5 6 Bxd5 Nxd5 7 dxc5 Ndb4 8 a3 Qxd1+ 9 Kxd1 Na6 10 b4. Although I have managed that each time as Black, the prospect of having to do so repetitively is profoundly unappealing.
So I've switched to my second string: the Ulvestad Variation. An online thematic tournament prompted me to go through published theory with Stockfish which turned up quite a lot of interesting ideas. Ultimately, Black may still be obliged to defend pawn-down endgames, but I think there are excellent prospects for success."
Well my recommendation is to learn the Traxler counter attack, it can score a lot of brilliancies.
Looks like an interesting (and rare) option. Thanks!
See my book for more details
https://everymanchess.com/products/a-disreputable-opening-repertoire
...in which you get a mention btw...
"I was intending initially to write about the Traxler, my main weapon for over thirty years. Unfortunately, issues have arisen with 4...Bc5, not least 5 d4! for which IM Panayotis Frendzas has been proselytizing online. It seems the best Black can do is to try to defend a dreary endgame a pawn down after 5...d5 6 Bxd5 Nxd5 7 dxc5 Ndb4 8 a3 Qxd1+ 9 Kxd1 Na6 10 b4. Although I have managed that each time as Black, the prospect of having to do so repetitively is profoundly unappealing.
So I've switched to my second string: the Ulvestad Variation. An online thematic tournament prompted me to go through published theory with Stockfish which turned up quite a lot of interesting ideas. Ultimately, Black may still be obliged to defend pawn-down endgames, but I think there are excellent prospects for success."
Thanks for the mention, although the first who noticed the strength of 5.d4 is FM Stefan Buecker, author of Kaissiber. I do hope he is fine, I've heard that he had some health issues.
And while 5.d4 is a very nice practical OTB choice, 5.Bxf7+ Ke7 6.Bc4 is close to being a direct refutation (me guesses you have seen the games of the ICCF WSTT/5/17/F thematic tournament, right?).
I see it is not "for sale" yet, at least not via the Everyman site. NIC ony has the paperback edition, to be honest I much prefer the cbv stuff.
Thanks for the mention, although the first who noticed the strength of 5.d4 is FM Stefan Buecker, author of Kaissiber. I do hope he is fine, I've heard that he had some health issues.
And while 5.d4 is a very nice practical OTB choice, 5.Bxf7+ Ke7 6.Bc4 is close to being a direct refutation (me guesses you have seen the games of the ICCF WSTT/5/17/F thematic tournament, right?).
I have the WSTT/5/17/F games in my database, yes – but I've not really looked at them. I've been doing so well with 5 d4 (P14, W12, D2, L0), I've not had the need to look at anything else
Yes, I've seen Stefan's stuff on 5 d4. Though perhaps the first to give it an "!" was US master Albert Pinkus in 1941. I can't remember whether Stefan mentions Pinkus or not. Quite likely he does. He's very strong on chess history. Yes, I hope he's okay.
#21 yeah as if the Gioco Pianissimo, Evans Gambit and the Italian with c3 and d4 were a walk in the Park for black