What, 5... c6? I think I have to disagree with you. Sure, there is that mate threat if Nxe5. The thing is that something like Nc6 or Nd7 also stop 6. Nxe5. Nc6 seems to be a much more useful move in the long run.
Note that in the mainline, white trying this trick results in them losing a knight (and a bishop if they're stupid enough not to play Be2) for just a pawn.
This game became very cramped. Probably some risky moves played. Eventually I got black to trade off their rooks, which were their only moveable pieces. They then got their queen stuck behind my pawns allowing me to force a promotion. The types of positions in the middle of the game always are a bit confusing for me. Maybe someone can comment on things to do, plans, etc.