Possibly none. In a genuinely low-competition niche, a new site can rank with very few backlinks or even zero, because ranking is competition-relative and strong content can win wherever the existing pages are weak. There is no fixed minimum number of links that earns a ranking, so the honest answer is that the link bar is set by the niche, not by a rule. If the pages already ranking have thin content and no meaningful links, a well-built page can pass them on relevance and quality alone. Treat this as competition-relative working judgment rather than a promise.
The reason there is no universal number is that links are valued in comparison to your competitors, not against an absolute threshold. Search engines rank the best available result for a query, and “best” is judged relative to the field. If that field is full of authoritative sites with strong link profiles, you will likely need links of your own to compete. If the field is a handful of weak, lightly linked pages, the page that most thoroughly and clearly answers the query can win with little or no external endorsement. Same site, same content, different niche, completely different link requirement.
This is also why naming a fixed minimum (five links, ten links, twenty) misleads more than it helps. Any such number is true only for the specific competitive context it was observed in, and copying it into a different niche tells you nothing. The right unit of analysis is the link bar of the niche you actually want to rank in, which you can read directly by looking at who ranks now and how they got there, rather than by importing a figure from someone else’s results.
For your next target term, study the pages on the first page before you think about link building: check whether they are genuinely strong and well-linked or thin and weakly linked. If the bar is low, write the better page and watch whether quality alone earns the ranking, and only invest in backlinks once the existing competition proves it actually demands them.