When the difference actually is significant

Strategy A has an estimated edge of $5.0$ bp with standard error $1.0$ bp ($z_A = 5.0$, extremely significant). Strategy B has an estimated edge of $1.0$ bp with standard error $1.0$ bp ($z_B = 1.0$, not significant).

Test whether A's edge significantly exceeds B's, and explain why this case shows that you cannot skip the difference test even when it seems obvious.