Step 1: Anchor on the embryology timeline: the heart is the first organ to function, and its tube assembles in week $3$.
Step 2: Around day $22$ the tubular heart begins to beat, even before it is fully septated. Converting to weeks, this lands squarely in the $3$ to $5$ week band.
Step 3: The other choices miss the mark: at $10$ to $12$ days no heart tube exists yet, and $10$ to $12$ weeks or $3$ to $5$ months describe a heart that is already long active.
\[\boxed{\text{3 to 5 weeks}}\]