@mrbasso 5. ... exd4 is perfectly playable and the engine likes it. It has never been played in the Lichess Masters Database but that's mainly because this line is quite rare. 5. ... Nd7 is also a fine move here and is a bit more principled: Black's main edge lies in their big centre so it makes sense to try to support it as opposed to trading it away. I agree with you that I don't think that 5. ... e4 was good, though it has been played by titled players before.
@MrPushwood Perhaps I should provide some statistics. Of the 1935 games in the Lichess Masters database that start with 1. b4, in 971 of them (about 50%) Black responded with 1. ... e5. That of course means that Black has a 50% chance of doing something else (and there are some interesting sidelines like 1. b4 c6 with the idea of 2. ... a5 or 2. ... Qb6 that are worth learning about) but 1. ... e5 is the most critical line. If White doesn't know what they're doing in 1. b4 e5 then they can lose very quickly whereas the other lines are often more forgiving.
It is true though: one of the practical problems of playing the Sokolsky is that Black has many good choices including a choice between going for boring equality vs. going for dynamic equality. 1. b4 e5 is very popular among higher-rated opponents because it will often give Black the latter (or even better, an advantage if White doesn't know what they're doing).