This pseudo-Evans Gambit is a very poor move for white. Black should respond:
5...d5! 6.exd5 (6.bxc5 dxc4 7.Nc3 Bg4 8.Nf3 Nd4 and black is much better) 6...Nxb4 7.d6 (7.0-0 Bg4) 7...Qxd6 8.Bxf7+ (8.Nxf7 Qd4 9.0-0 Bg4 10.Qe1 Nxc2 and black wins) 8...Kf8 9.Bb3 (9.Nc3 Qc6) 9...Qd4 10.Qe2 Qxa1 11.Qc4 Bxf2+ and black wins.
Looks good now! It seems logical that this would be fine for Black, since the Evans is fine for Black but here the g8-Knight gets developed and White's compensating tempo is a second move of the same piece. Thanks for putting this line up, I've never heard of it before.
This article covers black's response to 5.b4.
5.b4
This pseudo-Evans Gambit is a very poor move for white. Black should respond:
5...d5! 6.exd5 (6.bxc5 dxc4 7.Nc3 Bg4 8.Nf3 Nd4 and black is much better) 6...Nxb4 7.d6 (7.0-0 Bg4) 7...Qxd6 8.Bxf7+ (8.Nxf7 Qd4 9.0-0 Bg4 10.Qe1 Nxc2 and black wins) 8...Kf8 9.Bb3 (9.Nc3 Qc6) 9...Qd4 10.Qe2 Qxa1 11.Qc4 Bxf2+ and black wins.