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The rulebook says,
10.16 EARNED RUNS AND RUNS ALLOWED

An earned run is a run for which a pitcher is held accountable. In determining earned runs, the official scorer shall reconstruct the inning without the errors (which exclude catcher’s interference) and passed balls, giving the benefit of the doubt always to the pitcher in determining which bases would have been reached by runners had there been errorless play. For the purpose of determining earned runs, an intentional base on balls, regardless of the circumstances, shall be construed in exactly the same manner as any other base on balls.

There is another page or so of examples, but this is the gist of it.

In your example, B1 is out #1, B2 is out #2, B3 hit - doesn't matter how many bases, B4 BB, (B3 & B4 on) B5 out #3, no runs score.

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