Step 1: Anchor on embryology timelines. The paired heart tubes appear and fuse during week three, making the heart the first functioning organ in the embryo.
Step 2: The newly formed tubular heart begins to beat spontaneously at about 22 to 23 days, well within the third-to-fifth-week band.
Step 3: The other choices fail the timeline. At 10 to 12 days the embryo is still at the bilaminar/early trilaminar stage with no heart. By 10 to 12 weeks or 3 to 5 months the four-chambered heart is long established. So the earliest contraction time matches 3 to 5 weeks.
\[\boxed{\text{3 to 5 weeks}}\]