That's the dilemma of single-member-district voting and staggered terms. District 5 is one of the more affluent districts, so it has attracted a surplus of candidates while a less affluent district, such as District 6, attracts fewer challengers. District 3 is also an affluent district but is not yet contested.
A push for minority representation on City Council produced this situation. Although at-large voting had elected two African-Americans to City Council (A.P. Coleman and Gwen Burton), the federal Voting Rights Act favors majority-minority districts, which virtually guarantee minority representation, and the city switched to single-member districts in the 1980s. Three districts are white-majority and three are black-majority with one district, District 6, closely divided between the races. The only official elected citywide is the mayor.
Wilson is nearly evenly divided by race with minorities holding a slight edge in population. But changing back to at-large elections is politically unfeasible. Although some council members will say privately that they'd like to see at least some at-large districts (Raleigh, for example, uses a mixture of at-large and single-member districts), there has never been a serious effort to change the election law, which would have to be approved by the U.S. Justice Department.
A change to three at-large districts and four single-member districts (two white-majority and two black-majority) would increase voter clout and offer candidates more options — they could seek either an at-large or a district seat. My guess is that, depending on which candidates run, Wilson would end up with four white and three black council members, the same split we have now, but a black-majority council would be possible. The biggest advantage to this scenario is that the at-large candidates would have to appeal to both black and white voters. (Changing to concurrent rather than staggered terms — i.e., every seat is contested every two or four years — would give voters a chance to turn out the entire council in one election.)
That's not going to happen, least of all this year. The three challengers in District 5 are good news for incumbent Donald Evans. An incumbent enters an election with an advantage in name recognition and electoral experience. A challenger has to give voters a reason to not vote for the incumbent. When multiple candidates divide the anti-incumbent vote, guess who wins. If, however, those three District 5 challengers were scattered among at-large districts, one or more of them might win.
Until four members of City Council see an advantage in changing to at-large elections, change will never happen. Because district elections work to incumbents' advantage (see above), that's not likely to ever happen.