I think that the fact you stated that it is a "colony ship" auto-negates the "omg! Decay to the stone age in ten years!" scenario. A COLONY ship would be equipped to establish a COLONY. That means it wouldn't be packed with the 23rd century version of ignorant valley girls and frat boys. Look at the training modern astronauts have to go through just to float above earth for a bit and maybe spacewalk. I'd wager that a colonist would be a mid-late 20s fertile individual who, regardless of sexual orientation, aggrees to participate in manual population growth until fertilization clinics can be established AND has completed the equivalent of a doctoral course including:
Technological interrelated history (like the old tv show "Connections" but on a much deeper level),
Staggered specialization (medical, mechanics, applied sciences, etc. And each colonist would have a primary specialty),
Overlapping familiarity with several other specialties.
Likewise, the colonization process would be planned, not improvised:
The colony ship would probably be designed to at the very least be cannibalized for shelters and machinery construction, if not designed to permanently land and become a small city/fortress at the colony's core once scout craft found its landing site. The ship's reactor would become the planet's first power plant. Engines vecome turbines to generate additional power or perform rapid excavation. Birthing becomes sheltered lodging. Hydroponics is now a giant greenhouse with preestablished familiar flora. Medical bay is an instant hospital . . . you get the idea.
After initial food, shelter, and safety are started, the very next project would be population control. Long before they boarded, each colonist should have a paired mate, and the couple assigned a place in rotation for reproduction. Especially once they know they have been cut off from emigrants/reinforcements, breeding becomes a matter of the group's survival, and would be kept as a priority at least through the first generation.
Your 5000 arrivals would likely close to double their number (each couple having roughly 4 children in a span of 10-15 years of remaining fertility is not unreasonable if it is a focus of the group as a whole). After that, population would still probably be at least that of 19th century England. Another part of that preparedness would probably include the medical knowledge of now+200 years having packed along some rather reliable fertility treatments.
Add to that the fact that your colonists could easily have the knowledge (or have come up with it in another 600 years) to create cloning facilities and artificial wombs . . .the 12 million estimate is conservative. You could just about make them have spread to numerous sub-colonies by now, and could number in the 10s or even hundreds of millions.